Crampé, Nicolas; Gaboriaud, Julien; Poulain d’Andecy, Loïc; Vinet, Luc Matrix elements of \(SO(3)\) in \(sl_3\) representations as bispectral multivariate functions. (English) Zbl 07774846 J. Math. Phys. 64, No. 11, Article ID 111702, 16 p. (2023). MSC: 33C80 81R12 33D45 81R05 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Math. Phys. 64, No. 11, Article ID 111702, 16 p. (2023; Zbl 07774846) Full Text: DOI arXiv
Pelletier, Jonathan; Vinet, Luc; Zhedanov, Alexei Para-Bannai-Ito polynomials. (English) Zbl 07773352 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 090, 19 p. (2023). MSC: 33C47 33E30 47B39 47E07 PDFBibTeX XMLCite \textit{J. Pelletier} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 090, 19 p. (2023; Zbl 07773352) Full Text: DOI arXiv
Chea, Vutha Vichhea; Vinet, Luc; Zaimi, Meri; Zhedanov, Alexei An algebraic treatment of the Pastro polynomials on the real line. (English) Zbl 07741070 Proc. Am. Math. Soc. 151, No. 10, 4405-4418 (2023). MSC: 39A13 39A70 33D45 47B36 05A30 PDFBibTeX XMLCite \textit{V. V. Chea} et al., Proc. Am. Math. Soc. 151, No. 10, 4405--4418 (2023; Zbl 07741070) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei The rational Heun operator and Wilson biorthogonal functions. (English) Zbl 07690247 Ramanujan J. 61, No. 1, 7-29 (2023). MSC: 33D45 33C47 47B36 42C05 39A70 39A13 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Ramanujan J. 61, No. 1, 7--29 (2023; Zbl 07690247) Full Text: DOI arXiv
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc The single-indexed exceptional Krawtchouk polynomials. (English) Zbl 07686655 J. Difference Equ. Appl. 29, No. 3, 344-365 (2023). Reviewer: Ahmad Barhoumi (Stockholm) MSC: 33C45 44A55 39A70 PDFBibTeX XMLCite \textit{H. Miki} et al., J. Difference Equ. Appl. 29, No. 3, 344--365 (2023; Zbl 07686655) Full Text: DOI arXiv
Crampé, Nicolas; Poulain d’Andecy, Loïc; Vinet, Luc; Zaimi, Meri Askey-Wilson braid algebra and centralizer of \(U_q (\mathfrak{sl}_2)\). (English) Zbl 07685694 Ann. Henri Poincaré 24, No. 6, 1897-1922 (2023). MSC: 17B37 81R50 33C45 PDFBibTeX XMLCite \textit{N. Crampé} et al., Ann. Henri Poincaré 24, No. 6, 1897--1922 (2023; Zbl 07685694) Full Text: DOI arXiv
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei The rational Sklyanin algebra and the Wilson and para-Racah polynomials. (English) Zbl 1508.17016 J. Math. Phys. 63, No. 6, Article ID 061704, 14 p. (2022). MSC: 17B37 33C45 33C47 33C80 PDFBibTeX XMLCite \textit{G. Bergeron} et al., J. Math. Phys. 63, No. 6, Article ID 061704, 14 p. (2022; Zbl 1508.17016) Full Text: DOI arXiv
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials. (English) Zbl 1507.82017 J. Math. Phys. 63, No. 10, Article ID 103502, 16 p. (2022). MSC: 82B20 33C45 42C05 81P45 33C47 26A33 PDFBibTeX XMLCite \textit{H. Miki} et al., J. Math. Phys. 63, No. 10, Article ID 103502, 16 p. (2022; Zbl 1507.82017) Full Text: DOI arXiv
Bernard, Pierre-Antoine; Crampé, Nicolas; Vinet, Luc Time and band limiting operator and Bethe ansatz. (English) Zbl 1507.81110 J. Phys. A, Math. Theor. 55, No. 28, Article ID 285201, 15 p. (2022). MSC: 81Q80 81U15 82B23 33C47 PDFBibTeX XMLCite \textit{P.-A. Bernard} et al., J. Phys. A, Math. Theor. 55, No. 28, Article ID 285201, 15 p. (2022; Zbl 1507.81110) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Free boson realization of the Dunkl intertwining operator in one dimension. (English) Zbl 1513.81074 Rev. Math. Phys. 34, No. 8, Article ID 2250025, 12 p. (2022). MSC: 81Q80 33C45 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Rev. Math. Phys. 34, No. 8, Article ID 2250025, 12 p. (2022; Zbl 1513.81074) Full Text: DOI arXiv
Bussière, Ismaël; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Bispectrality and biorthogonality of the rational functions of \(q\)-Hahn type. (English) Zbl 1519.33012 J. Math. Anal. Appl. 516, No. 1, Article ID 126443, 17 p. (2022). MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{I. Bussière} et al., J. Math. Anal. Appl. 516, No. 1, Article ID 126443, 17 p. (2022; Zbl 1519.33012) Full Text: DOI arXiv
Crampé, Nicolas; Vinet, Luc; Zaimi, Meri Braid group and \(q\)-Racah polynomials. (English) Zbl 1486.17025 Proc. Am. Math. Soc. 150, No. 3, 951-966 (2022). Reviewer: Dmitry Artamonov (Moskva) MSC: 17B37 20F36 33C45 PDFBibTeX XMLCite \textit{N. Crampé} et al., Proc. Am. Math. Soc. 150, No. 3, 951--966 (2022; Zbl 1486.17025) Full Text: DOI arXiv
Beaudoin, André; Bergeron, Geoffroy; Brillant, Antoine; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Orthogonal polynomials and the deformed Jordan plane. (English) Zbl 1491.33009 J. Math. Anal. Appl. 507, No. 1, Article ID 125717, 10 p. (2022). MSC: 33C47 PDFBibTeX XMLCite \textit{A. Beaudoin} et al., J. Math. Anal. Appl. 507, No. 1, Article ID 125717, 10 p. (2022; Zbl 1491.33009) Full Text: DOI arXiv
Pelletier, Jonathan; Vinet, Luc; Zhedanov, Alexei Continuous \(-1\) Hypergeometric Orthogonal Polynomials. arXiv:2209.10727 Preprint, arXiv:2209.10727 [math.CA] (2022). MSC: 33C47 BibTeX Cite \textit{J. Pelletier} et al., ``Continuous $-1$ Hypergeometric Orthogonal Polynomials'', Preprint, arXiv:2209.10727 [math.CA] (2022) Full Text: arXiv OA License
Vinet, Luc; Zaimi, Meri; Zhedanov, Alexei \(R_I\) biorthogonal polynomials of Hahn type. arXiv:2209.07433 Preprint, arXiv:2209.07433 [math.CA] (2022). MSC: 33C47 33C45 47B36 BibTeX Cite \textit{L. Vinet} et al., ``$R_I$ biorthogonal polynomials of Hahn type'', Preprint, arXiv:2209.07433 [math.CA] (2022) Full Text: arXiv OA License
Crampé, Nicolas; Frappat, Luc; Gaboriaud, Julien; Poulain d’Andecy, Loïc; Ragoucy, Eric; Vinet, Luc The Askey-Wilson algebra and its avatars. (English) Zbl 1519.81276 J. Phys. A, Math. Theor. 54, No. 6, Article ID 063001, 32 p. (2021). MSC: 81R05 33D45 17B37 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Phys. A, Math. Theor. 54, No. 6, Article ID 063001, 32 p. (2021; Zbl 1519.81276) Full Text: DOI arXiv
De Bie, Hendrik; Iliev, Plamen; van de Vijver, Wouter; Vinet, Luc The Racah algebra: an overview and recent results. (English) Zbl 1497.81062 Adamović, Dražen (ed.) et al., Lie groups, number theory, and vertex algebras. Representation theory XVI. Conference, Inter-University Center, Dubrovnik, Croatia, June 24–29, 2019. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 768, 3-20 (2021). MSC: 81R12 33C45 33C80 33C50 17B10 PDFBibTeX XMLCite \textit{H. De Bie} et al., Contemp. Math. 768, 3--20 (2021; Zbl 1497.81062) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei An algebraic treatment of the Askey biorthogonal polynomials on the unit circle. (English) Zbl 1528.33016 Forum Math. Sigma 9, Paper No. e68, 28 p. (2021). MSC: 33C47 33C80 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Forum Math. Sigma 9, Paper No. e68, 28 p. (2021; Zbl 1528.33016) Full Text: DOI arXiv
Crampé, Nicolas; Kabakibo, Dounia Shaaban; Vinet, Luc New realizations of algebras of the Askey-Wilson type in terms of Lie and quantum algebras. (English) Zbl 1486.33019 Rev. Math. Phys. 33, No. 2, Article ID 2150002, 15 p. (2021). MSC: 33C80 17B37 81R50 PDFBibTeX XMLCite \textit{N. Crampé} et al., Rev. Math. Phys. 33, No. 2, Article ID 2150002, 15 p. (2021; Zbl 1486.33019) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane Howe duality and algebras of the Askey-Wilson type: an overview. (English) Zbl 1492.17015 Paranjape, M. B. (ed.) et al., Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1–5, 2019. Cham: Springer. CRM Ser. Math. Phys., 225-233 (2021). Reviewer: Dwight Williams II (New York) MSC: 17B37 16T20 17A45 17A70 33C52 81R05 33D45 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., in: Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1--5, 2019. Cham: Springer. 225--233 (2021; Zbl 1492.17015) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei A unified algebraic underpinning for the Hahn polynomials and rational functions. (English) Zbl 1459.33010 J. Math. Anal. Appl. 497, No. 1, Article ID 124863, 34 p. (2021). Reviewer: Michael Voit (Dortmund) MSC: 33C80 33C45 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Math. Anal. Appl. 497, No. 1, Article ID 124863, 34 p. (2021; Zbl 1459.33010) Full Text: DOI arXiv
Bergeron, Geoffroy; Gaboriaud, Julien; Vinet, Luc; Zhedanov, Alexei Sklyanin-like algebras for \((q\)-)linear grids and \((q\)-)para-Krawtchouk polynomials. (English) Zbl 1456.81265 J. Math. Phys. 62, No. 1, Article ID 013505, 20 p. (2021). MSC: 81R50 17B37 47B40 33D45 PDFBibTeX XMLCite \textit{G. Bergeron} et al., J. Math. Phys. 62, No. 1, Article ID 013505, 20 p. (2021; Zbl 1456.81265) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type. (English) Zbl 1456.33011 Proc. Am. Math. Soc. 149, No. 2, 715-728 (2021). Reviewer: Francisco Marcellán (Leganes) MSC: 33C45 33C80 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Proc. Am. Math. Soc. 149, No. 2, 715--728 (2021; Zbl 1456.33011) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei A note on \(\mathfrak{su}(2)\) models and the biorthogonality of generating functions of Krawtchouk polynomials. arXiv:2104.01430 Preprint, arXiv:2104.01430 [math.RT] (2021). MSC: 33C45 17B10 41A21 BibTeX Cite \textit{L. Vinet} and \textit{A. Zhedanov}, ``A note on $\mathfrak{su}(2)$ models and the biorthogonality of generating functions of Krawtchouk polynomials'', Preprint, arXiv:2104.01430 [math.RT] (2021) Full Text: arXiv OA License
Gaboriaud, Julien; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Degenerate Sklyanin algebras, Askey-Wilson polynomials and Heun operators. (English) Zbl 1519.81279 J. Phys. A, Math. Theor. 53, No. 44, Article ID 445204, 19 p. (2020). MSC: 81R05 33D45 14A22 16S38 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 53, No. 44, Article ID 445204, 19 p. (2020; Zbl 1519.81279) Full Text: DOI arXiv
Luo, Yu; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Dunkl-supersymmetric orthogonal functions associated with classical orthogonal polynomials. (English) Zbl 1514.42032 J. Phys. A, Math. Theor. 53, No. 8, Article ID 085205, 17 p. (2020). MSC: 42C05 33C45 81Q60 PDFBibTeX XMLCite \textit{Y. Luo} et al., J. Phys. A, Math. Theor. 53, No. 8, Article ID 085205, 17 p. (2020; Zbl 1514.42032) Full Text: DOI arXiv
Chan, Ada; Coutinho, Gabriel; Tamon, Christino; Vinet, Luc; Zhan, Hanmeng Fractional revival and association schemes. (English) Zbl 1447.05242 Discrete Math. 343, No. 11, Article ID 112018, 15 p. (2020). MSC: 05E30 42C05 PDFBibTeX XMLCite \textit{A. Chan} et al., Discrete Math. 343, No. 11, Article ID 112018, 15 p. (2020; Zbl 1447.05242) Full Text: DOI arXiv
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc Spin chains, graphs and state revival. (English) Zbl 1443.33021 Foupouagnigni, Mama (ed.) et al., Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser. Tutor. Sch. Workshops Math. Sci., 495-516 (2020). MSC: 33C45 81R30 PDFBibTeX XMLCite \textit{H. Miki} et al., in: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5--12, 2018. Cham: Birkhäuser. 495--516 (2020; Zbl 1443.33021) Full Text: DOI arXiv
Bergeron, Geoffroy; Vinet, Luc; Zhedanov, Alexei Signal processing, orthogonal polynomials, and Heun equations. (English) Zbl 1443.33033 Foupouagnigni, Mama (ed.) et al., Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser. Tutor. Sch. Workshops Math. Sci., 195-214 (2020). MSC: 33C80 94A11 PDFBibTeX XMLCite \textit{G. Bergeron} et al., in: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5--12, 2018. Cham: Birkhäuser. 195--214 (2020; Zbl 1443.33033) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Ragoucy, Eric; Vinet, Luc The dual pair \((U_q(\mathfrak{s} \mathfrak{u}(1, 1)), \mathfrak{o}_{q^{1 / 2}}(2 n)),q\)-oscillators, and Askey-Wilson algebras. (English) Zbl 1443.81042 J. Math. Phys. 61, No. 4, 041701, 11 p. (2020). MSC: 81R50 33D45 22E70 81T55 81R05 PDFBibTeX XMLCite \textit{L. Frappat} et al., J. Math. Phys. 61, No. 4, 041701, 11 p. (2020; Zbl 1443.81042) Full Text: DOI arXiv
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei The q-Heun operator of big q-Jacobi type and the q-Heun algebra. (English) Zbl 1444.39007 Ramanujan J. 52, No. 2, 367-380 (2020). Reviewer: Lalit Mohan Upadhyaya (Mussoorie) MSC: 39A13 39A70 33D05 33E30 33C45 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Ramanujan J. 52, No. 2, 367--380 (2020; Zbl 1444.39007) Full Text: DOI arXiv
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra. (English) Zbl 1436.81070 Ramanujan J. 51, No. 3, 629-648 (2020). MSC: 81R50 81R10 81U15 39A70 33D50 39A13 17B37 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Ramanujan J. 51, No. 3, 629--648 (2020; Zbl 1436.81070) Full Text: DOI arXiv
Crampé, Nicolas; Vinet, Luc; Zhedanov, Alexei Heun algebras of Lie type. (English) Zbl 1452.17024 Proc. Am. Math. Soc. 148, No. 3, 1079-1094 (2020). Reviewer: Dmitry Artamonov (Moskva) MSC: 17B60 33C45 33C80 PDFBibTeX XMLCite \textit{N. Crampé} et al., Proc. Am. Math. Soc. 148, No. 3, 1079--1094 (2020; Zbl 1452.17024) Full Text: DOI arXiv
Crampé, Nicolas; Ragoucy, Eric; Vinet, Luc; Zhedanov, Alexei Truncation of the reflection algebra and the Hahn algebra. (English) Zbl 1509.17009 J. Phys. A, Math. Theor. 52, No. 35, Article ID 35LT01, 10 p. (2019). MSC: 17B37 17B80 33C45 20F55 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Phys. A, Math. Theor. 52, No. 35, Article ID 35LT01, 10 p. (2019; Zbl 1509.17009) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The Higgs and Hahn algebras from a Howe duality perspective. (English) Zbl 1476.81035 Phys. Lett., A 383, No. 14, 1531-1535 (2019). MSC: 81Q05 81Q35 42C05 14M27 37K10 PDFBibTeX XMLCite \textit{L. Frappat} et al., Phys. Lett., A 383, No. 14, 1531--1535 (2019; Zbl 1476.81035) Full Text: DOI arXiv
Crampé, Nicolas; Nepomechie, Rafael I.; Vinet, Luc Free-fermion entanglement and orthogonal polynomials. (English) Zbl 1456.81058 J. Stat. Mech. Theory Exp. 2019, No. 9, Article ID 093101, 17 p. (2019). MSC: 81P40 82B20 33C45 33D45 PDFBibTeX XMLCite \textit{N. Crampé} et al., J. Stat. Mech. Theory Exp. 2019, No. 9, Article ID 093101, 17 p. (2019; Zbl 1456.81058) Full Text: DOI arXiv
Frappat, Luc; Gaboriaud, Julien; Ragoucy, Eric; Vinet, Luc The \(q\)-Higgs and Askey-Wilson algebras. (English) Zbl 1430.81042 Nucl. Phys., B 944, Article ID 114632, 13 p. (2019). MSC: 81R50 17B37 17B35 33D45 81Q35 81R05 PDFBibTeX XMLCite \textit{L. Frappat} et al., Nucl. Phys., B 944, Article ID 114632, 13 p. (2019; Zbl 1430.81042) Full Text: DOI arXiv
Koelink, Erik; Lemay, Jean-Michel; Vinet, Luc Convolution identities for Dunkl orthogonal polynomials from the \(\mathfrak{o} \mathfrak{s} \mathfrak{p}(1 | 2)\) Lie superalgebra. (English) Zbl 1422.33006 J. Math. Phys. 60, No. 9, 091701, 16 p. (2019). MSC: 33D80 33D45 33C45 33C80 33C20 17A70 16S40 PDFBibTeX XMLCite \textit{E. Koelink} et al., J. Math. Phys. 60, No. 9, 091701, 16 p. (2019; Zbl 1422.33006) Full Text: DOI arXiv
Genest, Vincent X.; Lapointe, Luc; Vinet, Luc \(\mathfrak{osp}(1,2)\) and generalized Bannai-Ito algebras. (English) Zbl 1482.17013 Trans. Am. Math. Soc. 372, No. 6, 4127-4148 (2019). Reviewer: Dwight Williams II (New York) MSC: 17A70 33C52 81R05 17B37 17B20 33D45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Trans. Am. Math. Soc. 372, No. 6, 4127--4148 (2019; Zbl 1482.17013) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle. (English) Zbl 1458.33008 Constr. Approx. 50, No. 2, 209-241 (2019). MSC: 33C80 20C08 33C45 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Constr. Approx. 50, No. 2, 209--241 (2019; Zbl 1458.33008) Full Text: DOI arXiv
Baseilhac, Pascal; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type. (English) Zbl 1423.33027 Ann. Henri Poincaré 20, No. 9, 3091-3112 (2019). MSC: 33D45 33C52 17A45 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Ann. Henri Poincaré 20, No. 9, 3091--3112 (2019; Zbl 1423.33027) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei The Heun operator of Hahn-type. (English) Zbl 1429.33018 Proc. Am. Math. Soc. 147, No. 7, 2987-2998 (2019). Reviewer: Manuel D. de la Iglesia (México D. F.) MSC: 33C45 33C80 39A70 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Proc. Am. Math. Soc. 147, No. 7, 2987--2998 (2019; Zbl 1429.33018) Full Text: DOI arXiv
Bergeron, G.; Koelink, E.; Vinet, L. \(\operatorname{SU}_q(3)\) corepresentations and bivariate \(q\)-Krawtchouk polynomials. (English) Zbl 1416.33025 J. Math. Phys. 60, No. 5, 051701, 13 p. (2019). Reviewer: P. K. Banerji (Jodhpur) MSC: 33D45 20G42 22E50 22E60 33D15 33D80 PDFBibTeX XMLCite \textit{G. Bergeron} et al., J. Math. Phys. 60, No. 5, 051701, 13 p. (2019; Zbl 1416.33025) Full Text: DOI arXiv
De Bie, Hendrik; Iliev, Plamen; Vinet, Luc Bargmann and Barut-Girardello models for the Racah algebra. (English) Zbl 1406.81046 J. Math. Phys. 60, No. 1, 011701, 13 p. (2019). MSC: 81R12 33C45 33C80 17B81 22E70 PDFBibTeX XMLCite \textit{H. De Bie} et al., J. Math. Phys. 60, No. 1, 011701, 13 p. (2019; Zbl 1406.81046) Full Text: DOI arXiv Link
Genest, Vincent X.; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei Supersymmetry of the quantum rotor. (English) Zbl 1411.33016 Nashed, M. Zuhair (ed.) et al., Frontiers in orthogonal polynomials and \(q\)-series. Papers based on the international conference, University of Central Florida, Orlando, FL, USA, May 10–12, 2015. Dedicated to Professor Mourad Ismail on his 70th birthday. Hackensack, NJ: World Scientific. Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 291-305 (2018). MSC: 33D45 17B37 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 291--305 (2018; Zbl 1411.33016) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc; Vinet, Stéphane; Zhedanov, Alexei The Racah algebra as a commutant and Howe duality. (English) Zbl 1411.81112 J. Phys. A, Math. Theor. 51, No. 50, Article ID 50LT01, 8 p. (2018). MSC: 81R12 33C45 17B67 22E70 37K10 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 51, No. 50, Article ID 50LT01, 8 p. (2018; Zbl 1411.81112) Full Text: DOI arXiv
Lemay, Jean-Michel; Vinet, Luc Bivariate Bannai-Ito polynomials. (English) Zbl 1423.33013 J. Math. Phys. 59, No. 12, 121703, 18 p. (2018). MSC: 33C45 05B30 33D45 PDFBibTeX XMLCite \textit{J.-M. Lemay} and \textit{L. Vinet}, J. Math. Phys. 59, No. 12, 121703, 18 p. (2018; Zbl 1423.33013) Full Text: DOI arXiv
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun operator and band-time limiting. (English) Zbl 1405.33025 Commun. Math. Phys. 364, No. 3, 1041-1068 (2018). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33D45 33D99 39B42 PDFBibTeX XMLCite \textit{F. A. Grünbaum} et al., Commun. Math. Phys. 364, No. 3, 1041--1068 (2018; Zbl 1405.33025) Full Text: DOI arXiv
Bergeron, Geoffroy; Vinet, Luc; Tsujimoto, Satoshi Generating function for the Bannai-Ito polynomials. (English) Zbl 1477.33013 Proc. Am. Math. Soc. 146, No. 12, 5077-5090 (2018). MSC: 33C45 22E70 81R05 PDFBibTeX XMLCite \textit{G. Bergeron} et al., Proc. Am. Math. Soc. 146, No. 12, 5077--5090 (2018; Zbl 1477.33013) Full Text: DOI arXiv
Baseilhac, Pascal; Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei An embedding of the Bannai-Ito algebra in \(\mathcal U(\mathfrak{osp}(1,2))\) and \(-1\) polynomials. (English) Zbl 1395.81126 Lett. Math. Phys. 108, No. 7, 1623-1634 (2018). MSC: 81R50 81Q80 81R10 33C45 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Lett. Math. Phys. 108, No. 7, 1623--1634 (2018; Zbl 1395.81126) Full Text: DOI arXiv
Gaboriaud, Julien; Vinet, Luc An algebraic interpretation of the \(q\)-Meixner polynomials. (English) Zbl 1390.33034 Ramanujan J. 46, No. 1, 127-149 (2018). MSC: 33D45 81R50 PDFBibTeX XMLCite \textit{J. Gaboriaud} and \textit{L. Vinet}, Ramanujan J. 46, No. 1, 127--149 (2018; Zbl 1390.33034) Full Text: DOI arXiv
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei A \(q\)-generalization of the para-Racah polynomials. (English) Zbl 1390.33035 J. Math. Anal. Appl. 462, No. 1, 323-336 (2018). MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{J.-M. Lemay} et al., J. Math. Anal. Appl. 462, No. 1, 323--336 (2018; Zbl 1390.33035) Full Text: DOI arXiv
Genest, Vincent X.; Iliev, Plamen; Vinet, Luc Coupling coefficients of \(\operatorname{su}_{q}(1,1)\) and multivariate \(q\)-Racah polynomials. (English) Zbl 1380.81166 Nucl. Phys., B 927, 97-123 (2018). MSC: 81R50 17B37 20G42 33C45 81R12 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Nucl. Phys., B 927, 97--123 (2018; Zbl 1380.81166) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei Symmetric abstract hypergeometric polynomials. (English) Zbl 1375.33022 J. Math. Anal. Appl. 458, No. 1, 742-754 (2018). MSC: 33C47 33C45 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., J. Math. Anal. Appl. 458, No. 1, 742--754 (2018; Zbl 1375.33022) Full Text: DOI arXiv
Bossé, Éric-Olivier; Vinet, Luc Coherent transport in photonic lattices: a survey of recent analytic results. (English) Zbl 1383.81044 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 074, 19 p. (2017). MSC: 81P45 33C45 81V80 PDFBibTeX XMLCite \textit{É.-O. Bossé} and \textit{L. Vinet}, SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 074, 19 p. (2017; Zbl 1383.81044) Full Text: DOI arXiv
Genest, Vincent X.; Post, Sarah; Vinet, Luc An algebraic interpretation of the multivariate \(q\)-Krawtchouk polynomials. (English) Zbl 1375.33031 Ramanujan J. 43, No. 2, 415-445 (2017). MSC: 33D45 16T05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Ramanujan J. 43, No. 2, 415--445 (2017; Zbl 1375.33031) Full Text: DOI arXiv
Genest, Vincent X.; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials. (English) Zbl 1375.65059 J. Math. Anal. Appl. 450, No. 2, 915-928 (2017). MSC: 65F18 33C45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Math. Anal. Appl. 450, No. 2, 915--928 (2017; Zbl 1375.65059) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Tridiagonal representations of the \(q\)-oscillator algebra and Askey-Wilson polynomials. (English) Zbl 1368.81074 J. Phys. A, Math. Theor. 50, No. 23, Article ID 235202, 15 p. (2017). MSC: 81Q10 17B81 33C45 33D45 47B36 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., J. Phys. A, Math. Theor. 50, No. 23, Article ID 235202, 15 p. (2017; Zbl 1368.81074) Full Text: DOI arXiv
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Tridiagonalization and the Heun equation. (English) Zbl 1364.34126 J. Math. Phys. 58, No. 3, 031703, 12 p. (2017). MSC: 34M03 34L40 34M35 47L30 33C45 34L15 PDFBibTeX XMLCite \textit{F. A. Grünbaum} et al., J. Math. Phys. 58, No. 3, 031703, 12 p. (2017; Zbl 1364.34126) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei Quantum spin chains with fractional revival. (English) Zbl 1380.82030 Ann. Phys. 371, 348-367 (2016). MSC: 82C20 81P45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Ann. Phys. 371, 348--367 (2016; Zbl 1380.82030) Full Text: DOI arXiv
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei An analytic spin chain model with fractional revival. (English) Zbl 1351.82044 J. Phys. A, Math. Theor. 49, No. 33, Article ID 335302, 15 p. (2016). MSC: 82C20 33C45 PDFBibTeX XMLCite \textit{J.-M. Lemay} et al., J. Phys. A, Math. Theor. 49, No. 33, Article ID 335302, 15 p. (2016; Zbl 1351.82044) Full Text: DOI arXiv
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. (English) Zbl 1351.33010 Proc. Am. Math. Soc. 144, No. 10, 4441-4454 (2016). Reviewer: Teresa A. Mesquita (Vila Nova de Famalicão) MSC: 33C45 33C80 42C05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Proc. Am. Math. Soc. 144, No. 10, 4441--4454 (2016; Zbl 1351.33010) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Hypergeometric orthogonal polynomials with respect to Newtonian bases. (English) Zbl 1341.42045 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 048, 14 p. (2016). MSC: 42C05 42C15 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 048, 14 p. (2016; Zbl 1341.42045) Full Text: DOI arXiv
Genest, Vincent X.; Post, Sarah; Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei \(q\)-rotations and Krawtchouk polynomials. (English) Zbl 1339.33020 Ramanujan J. 40, No. 2, 335-357 (2016). MSC: 33D45 16T05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Ramanujan J. 40, No. 2, 335--357 (2016; Zbl 1339.33020) Full Text: DOI arXiv
Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei The para-Racah polynomials. (English) Zbl 1333.33025 J. Math. Anal. Appl. 438, No. 2, 565-577 (2016). MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{J.-M. Lemay} et al., J. Math. Anal. Appl. 438, No. 2, 565--577 (2016; Zbl 1333.33025) Full Text: DOI arXiv
Vinet, Luc; Yu, Guo-Fu; Zhedanov, Alexei \(-1\) Krall-Jacobi polynomials. (English) Zbl 1327.33003 Methods Appl. Anal. 22, No. 3, 249-258 (2015). MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} et al., Methods Appl. Anal. 22, No. 3, 249--258 (2015; Zbl 1327.33003) Full Text: DOI arXiv
Gaboriaud, Julien; Genest, Vincent X.; Lemieux, Jessica; Vinet, Luc A superintegrable discrete oscillator and two-variable Meixner polynomials. (English) Zbl 1326.81090 J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015). MSC: 81Q80 33C80 39A14 33C50 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015; Zbl 1326.81090) Full Text: DOI arXiv
Genest, Vincent X.; Lemay, Jean-Michel; Vinet, Luc; Zhedanov, Alexei Two-variable -1 Jacobi polynomials. (English) Zbl 1317.33011 Integral Transforms Spec. Funct. 26, No. 6, 411-425 (2015). Reviewer: Bujar Fejzullahu (Presevo) MSC: 33C50 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Integral Transforms Spec. Funct. 26, No. 6, 411--425 (2015; Zbl 1317.33011) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc The generic superintegrable system on the 3-sphere and the \(9j\) symbols of \(\mathfrak{su}(1,1)\). (English) Zbl 1312.81096 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 108, 28 p. (2014). MSC: 81R05 33C50 22D20 15B48 15A21 PDFBibTeX XMLCite \textit{V. X. Genest} and \textit{L. Vinet}, SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 108, 28 p. (2014; Zbl 1312.81096) Full Text: DOI arXiv EMIS
Genest, Vincent X.; Vinet, Luc The multivariate Hahn polynomials and the singular oscillator. (English) Zbl 1307.81034 J. Phys. A, Math. Theor. 47, No. 45, Article ID 455201, 39 p. (2014). MSC: 81Q05 33C50 81Q10 81R12 PDFBibTeX XMLCite \textit{V. X. Genest} and \textit{L. Vinet}, J. Phys. A, Math. Theor. 47, No. 45, Article ID 455201, 39 p. (2014; Zbl 1307.81034) Full Text: DOI arXiv
Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Bannai-Ito polynomials and dressing chains. (English) Zbl 1304.42063 Proc. Am. Math. Soc. 142, No. 12, 4191-4206 (2014). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 42C05 17B80 33C45 47B36 PDFBibTeX XMLCite \textit{M. Derevyagin} et al., Proc. Am. Math. Soc. 142, No. 12, 4191--4206 (2014; Zbl 1304.42063) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei Superintegrability in two dimensions and the Racah-Wilson algebra. (English) Zbl 1311.81145 Lett. Math. Phys. 104, No. 8, 931-952 (2014). Reviewer: Willard Miller jun. (Minneapolis) MSC: 81R12 33C45 22E70 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Lett. Math. Phys. 104, No. 8, 931--952 (2014; Zbl 1311.81145) Full Text: DOI arXiv
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei The multivariate Charlier polynomials as matrix elements of the Euclidean group representation on oscillator states. (English) Zbl 1296.33025 J. Phys. A, Math. Theor. 47, No. 21, Article ID 215204, 16 p. (2014). Reviewer: József Sándor (Cluj-Napoca) MSC: 33C50 06B15 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 47, No. 21, Article ID 215204, 16 p. (2014; Zbl 1296.33025) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei A “continuous” limit of the complementary Bannai-Itô polynomials: Chihara polynomials. (English) Zbl 1293.33012 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 038, 18 p. (2014). MSC: 33C45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 038, 18 p. (2014; Zbl 1293.33012) Full Text: DOI arXiv EMIS
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei The multivariate Meixner polynomials as matrix elements of \(SO(d, 1)\) representations on oscillator states. (English) Zbl 1285.81023 J. Phys. A, Math. Theor. 47, No. 4, Article ID 045207, 18 p. (2014). MSC: 81Q10 81R05 33E30 81R15 20C35 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 47, No. 4, Article ID 045207, 18 p. (2014; Zbl 1285.81023) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei The Bannai-Ito polynomials as Racah coefficients of the \(sl_{-1}(2)\) algebra. (English) Zbl 1304.17019 Proc. Am. Math. Soc. 142, No. 5, 1545-1560 (2014). MSC: 17B80 33C45 33C47 81R05 16T05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Proc. Am. Math. Soc. 142, No. 5, 1545--1560 (2014; Zbl 1304.17019) Full Text: DOI arXiv
Miki, Hiroshi; Post, Sarah; Vinet, Luc; Zhedanov, Alexei A finite model of the oscillator in two-dimensions with \(SU(2)\) symmetry. (English) Zbl 1297.81074 Bai, Chengming (ed.) et al., Symmetries and groups in contemporary physics. Proceedings of the XXIX international colloquium on group-theoretical methods in physics, Tianjin, China, August 20–26, 2012. Hackensack, NJ: World Scientific (ISBN 978-981-4518-54-3/hbk; 978-981-4518-56-7/ebook). Nankai Series in Pure, Applied Mathematics and Theoretical Physics 11, 217-222 (2013). MSC: 81Q05 22E70 81R05 33C45 PDFBibTeX XMLCite \textit{H. Miki} et al., Nankai Ser. Pure Appl. Math. Theor. Phys. 11, 217--222 (2013; Zbl 1297.81074) Full Text: DOI
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei The algebra of dual \(-1\) Hahn polynomials and the Clebsch-Gordan problem of \(\mathfrak{sl}_{-1}(2)\). (English) Zbl 1280.81071 J. Math. Phys. 54, No. 2, 023506, 13 p. (2013). MSC: 81R50 17B37 81R05 42C05 16T05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Math. Phys. 54, No. 2, 023506, 13 p. (2013; Zbl 1280.81071) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei The multivariate Krawtchouk polynomials as matrix elements of the rotation group representations on oscillator states. (English) Zbl 1282.22008 J. Phys. A, Math. Theor. 46, No. 50, Article ID 505203, 24 p. (2013). MSC: 22E46 06B15 33C50 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 46, No. 50, Article ID 505203, 24 p. (2013; Zbl 1282.22008) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei The singular and the 2:1 anisotropic Dunkl oscillators in the plane. (English) Zbl 1273.81089 J. Phys. A, Math. Theor. 46, No. 32, Article ID 325201, 17 p. (2013). MSC: 81Q10 81Q05 33C45 81R05 22E70 81R12 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 46, No. 32, Article ID 325201, 17 p. (2013; Zbl 1273.81089) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei Bispectrality of the complementary Bannai-Itō polynomials. (English) Zbl 1272.33010 SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 018, 20 p. (2013). MSC: 33C45 33C47 33C80 PDFBibTeX XMLCite \textit{V. X. Genest} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 018, 20 p. (2013; Zbl 1272.33010) Full Text: DOI arXiv
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. (English) Zbl 1267.81139 J. Phys. A, Math. Theor. 46, No. 14, Article ID 145201, 21 p. (2013). MSC: 81Q05 81R12 22E70 33C45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 46, No. 14, Article ID 145201, 21 p. (2013; Zbl 1267.81139) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Dual \(-1\) Hahn polynomials: “classical” polynomials beyond the Leonard duality. (English) Zbl 1300.33018 Proc. Am. Math. Soc. 141, No. 3, 959-970 (2013). Reviewer: Carsten Schneider (Linz) MSC: 33C45 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Proc. Am. Math. Soc. 141, No. 3, 959--970 (2013; Zbl 1300.33018) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei A limit \(q=-1\) for the big \(q\)-Jacobi polynomials. (English) Zbl 1276.33019 Trans. Am. Math. Soc. 364, No. 10, 5491-5507 (2012). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C47 42C05 33C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Trans. Am. Math. Soc. 364, No. 10, 5491--5507 (2012; Zbl 1276.33019) Full Text: DOI arXiv
Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei CMV matrices and little and big \(-1\) Jacobi polynomials. (English) Zbl 1259.42018 Constr. Approx. 36, No. 3, 513-535 (2012). Reviewer: Peter Massopust (München) MSC: 42C05 33C45 47B36 PDFBibTeX XMLCite \textit{M. Derevyagin} et al., Constr. Approx. 36, No. 3, 513--535 (2012; Zbl 1259.42018) Full Text: DOI arXiv
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc Families of superintegrable Hamiltonians constructed from exceptional polynomials. (English) Zbl 1255.81145 J. Phys. A, Math. Theor. 45, No. 40, Article ID 405202, 10 p. (2012). MSC: 81Q05 15A18 33D45 34K06 81R12 PDFBibTeX XMLCite \textit{S. Post} et al., J. Phys. A, Math. Theor. 45, No. 40, Article ID 405202, 10 p. (2012; Zbl 1255.81145) Full Text: DOI arXiv
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei An algebraic model for the multiple Meixner polynomials of the first kind. (English) Zbl 1251.81053 J. Phys. A, Math. Theor. 45, No. 32, Article ID 325205, 11 p. (2012). MSC: 81R30 20C35 42C05 33C80 81R10 81R15 PDFBibTeX XMLCite \textit{H. Miki} et al., J. Phys. A, Math. Theor. 45, No. 32, Article ID 325205, 11 p. (2012; Zbl 1251.81053) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer. (English) Zbl 1251.81021 J. Phys. A, Math. Theor. 45, No. 26, Article ID 265304, 11 p. (2012). MSC: 81P45 82B20 33C90 81U15 33C45 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Phys. A, Math. Theor. 45, No. 26, Article ID 265304, 11 p. (2012; Zbl 1251.81021) Full Text: DOI arXiv
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei \(d\)-orthogonal polynomials and \(\mathfrak {su}(2)\). (English) Zbl 1238.33004 J. Math. Anal. Appl. 390, No. 2, 472-487 (2012). MSC: 33C45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Math. Anal. Appl. 390, No. 2, 472--487 (2012; Zbl 1238.33004) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Dunkl shift operators and Bannai-Ito polynomials. (English) Zbl 1248.33022 Adv. Math. 229, No. 4, 2123-2158 (2012). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Adv. Math. 229, No. 4, 2123--2158 (2012; Zbl 1248.33022) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei Jordan algebras and orthogonal polynomials. (English) Zbl 1272.17031 J. Math. Phys. 52, No. 10, 103512, 8 p. (2011). MSC: 17C50 33C45 33D45 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., J. Math. Phys. 52, No. 10, 103512, 8 p. (2011; Zbl 1272.17031) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra. (English) Zbl 1246.17022 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 093, 13 p. (2011). MSC: 17B37 16T05 33C45 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 093, 13 p. (2011; Zbl 1246.17022) Full Text: DOI arXiv
Post, Sarah; Vinet, Luc; Zhedanov, Alexei An infinite family of superintegrable Hamiltonians with reflection in the plane. (English) Zbl 1238.81138 J. Phys. A, Math. Theor. 44, No. 50, Article ID 505201, 18 p. (2011). MSC: 81R12 81Q05 33C45 81Q10 PDFBibTeX XMLCite \textit{S. Post} et al., J. Phys. A, Math. Theor. 44, No. 50, Article ID 505201, 18 p. (2011; Zbl 1238.81138) Full Text: DOI arXiv
Post, Sarah; Vinet, Luc; Zhedanov, Alexei Supersymmetric quantum mechanics with reflections. (English) Zbl 1230.81032 J. Phys. A, Math. Theor. 44, No. 43, Article ID 435301, 15 p. (2011). MSC: 81Q60 15A18 33D45 PDFBibTeX XMLCite \textit{S. Post} et al., J. Phys. A, Math. Theor. 44, No. 43, Article ID 435301, 15 p. (2011; Zbl 1230.81032) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Representations of the Schrödinger group and matrix orthogonal polynomials. (English) Zbl 1227.81173 J. Phys. A, Math. Theor. 44, No. 35, Article ID 355201, 28 p. (2011). MSC: 81Q05 81R30 42C05 33C80 81R05 34C14 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Phys. A, Math. Theor. 44, No. 35, Article ID 355201, 28 p. (2011; Zbl 1227.81173) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei A Bochner theorem for Dunkl polynomials. (English) Zbl 1217.33022 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 020, 9 p. (2011). MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 020, 9 p. (2011; Zbl 1217.33022) Full Text: DOI arXiv EuDML
Vinet, Luc; Zhedanov, Alexei A ’missing’ family of classical orthogonal polynomials. (English) Zbl 1222.33011 J. Phys. A, Math. Theor. 44, No. 8, Article ID 085201, 16 p. (2011). Reviewer: Sunil Dutt Purohit (Udaipur) MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Phys. A, Math. Theor. 44, No. 8, Article ID 085201, 16 p. (2011; Zbl 1222.33011) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Dual -1 Hahn polynomials and perfect state transfer. arXiv:1110.6477 Preprint, arXiv:1110.6477 [math-ph] (2011). MSC: 33C45 33C90 BibTeX Cite \textit{L. Vinet} and \textit{A. Zhedanov}, ``Dual -1 Hahn polynomials and perfect state transfer'', Preprint, arXiv:1110.6477 [math-ph] (2011) Full Text: DOI arXiv OA License
Vinet, Luc; Zhedanov, Alexei Automorphisms of the Heisenberg-Weyl algebra and \(d\)-orthogonal polynomials. (English) Zbl 1202.33018 J. Math. Phys. 50, No. 3, 033511, 19 pp. (2009). MSC: 33C47 22E70 33C45 33C80 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Math. Phys. 50, No. 3, 033511, 19 pp. (2009; Zbl 1202.33018) Full Text: DOI
Vinet, Luc; Zhedanov, Alexei Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials. (English) Zbl 1140.33006 J. Comput. Appl. Math. 211, No. 1, 45-56 (2008). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33D45 42C05 39A10 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Comput. Appl. Math. 211, No. 1, 45--56 (2008; Zbl 1140.33006) Full Text: DOI arXiv