Guin, Satyajit; Saurabh, Bipul On the Clebsch-Gordan coefficients for the quantum group \(U_q (2)\). (English) Zbl 07784764 Proc. Indian Acad. Sci., Math. Sci. 133, No. 2, Paper No. 44, 20 p. (2023). MSC: 58B32 33D45 33D80 16W99 PDFBibTeX XMLCite \textit{S. Guin} and \textit{B. Saurabh}, Proc. Indian Acad. Sci., Math. Sci. 133, No. 2, Paper No. 44, 20 p. (2023; Zbl 07784764) Full Text: DOI
Crampé, Nicolas; Frappat, Luc; Poulain D’Andecy, Loïc; Ragoucy, Eric The higher-rank Askey-Wilson algebra and its braid group automorphisms. (English) Zbl 07762636 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 077, 36 p. (2023). Reviewer: Cristian Vay (Córdoba) MSC: 16T10 33D45 81R12 PDFBibTeX XMLCite \textit{N. Crampé} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 077, 36 p. (2023; Zbl 07762636) Full Text: DOI arXiv
Huang, Hau-Wen; Wen, Chia-Yi A connection behind the Terwilliger algebras of \(H(D,2)\) and \(\frac{ 1}{ 2} H(D,2)\). (English) Zbl 07741937 J. Algebra 634, 456-479 (2023). Reviewer: Matthew Davis (New Concord) MSC: 16G30 16S30 05E30 33D45 PDFBibTeX XMLCite \textit{H.-W. Huang} and \textit{C.-Y. Wen}, J. Algebra 634, 456--479 (2023; Zbl 07741937) Full Text: DOI arXiv
Huang, Hau-Wen The Clebsch-Gordan rule for \(U(\mathfrak{sl}_2)\), the Krawtchouk algebras and the Hamming graphs. (English) Zbl 1512.05409 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 017, 19 p. (2023). MSC: 05E30 16G30 16S30 33D45 PDFBibTeX XMLCite \textit{H.-W. Huang}, SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 017, 19 p. (2023; Zbl 1512.05409) Full Text: DOI arXiv
Crampé, Nicolas; Frappat, Luc; Ragoucy, Eric Representations of the rank two Racah algebra and orthogonal multivariate polynomials. (English) Zbl 07661159 Linear Algebra Appl. 664, 165-215 (2023). Reviewer: Nenad Manojlović (Faro) MSC: 33C80 33C45 16G60 52B05 52B15 PDFBibTeX XMLCite \textit{N. Crampé} et al., Linear Algebra Appl. 664, 165--215 (2023; Zbl 07661159) Full Text: DOI arXiv
Ercolani, Nicholas M.; Waters, Patrick Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel-Appell polynomials. (English) Zbl 1497.05020 Random Matrices Theory Appl. 11, No. 4, Article ID 2250037, 152 p. (2022). MSC: 05A40 05C30 16T05 34M55 60B20 60C05 70S10 83E30 PDFBibTeX XMLCite \textit{N. M. Ercolani} and \textit{P. Waters}, Random Matrices Theory Appl. 11, No. 4, Article ID 2250037, 152 p. (2022; Zbl 1497.05020) Full Text: DOI arXiv
Koelink, Erik (ed.); Kolb, Stefan (ed.); Reshetikhin, Nicolai (ed.); Vlaar, Bart (ed.) Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7–11, 2020. (English) Zbl 1496.17001 Contemporary Mathematics 780. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6520-9/pbk; 978-1-4704-7134-7/ebook). xii, 347 p. (2022). MSC: 17-06 17B80 33C80 43A90 13-06 13A35 16S38 17B37 17B67 33C60 33C67 33D45 60J60 00B25 00B30 PDFBibTeX XMLCite \textit{E. Koelink} (ed.) et al., Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7--11, 2020. Providence, RI: American Mathematical Society (AMS) (2022; Zbl 1496.17001) Full Text: DOI
Toppan, Francesco First quantization of braided Majorana fermions. (English) Zbl 1497.81022 Nucl. Phys., B 980, Article ID 115834, 14 p. (2022). MSC: 81P40 81P45 81V72 81P16 81S08 16T05 17A70 33C52 18M15 PDFBibTeX XMLCite \textit{F. Toppan}, Nucl. Phys., B 980, Article ID 115834, 14 p. (2022; Zbl 1497.81022) Full Text: DOI arXiv
Saied, Jason A combinatorial formula for Sahi, Stokman, and Venkateswaran’s generalization of Macdonald polynomials. (English) Zbl 07537706 Adv. Math. 404, Part B, Article ID 108440, 51 p. (2022). MSC: 05E05 16S99 20C08 33C52 PDFBibTeX XMLCite \textit{J. Saied}, Adv. Math. 404, Part B, Article ID 108440, 51 p. (2022; Zbl 07537706) Full Text: DOI arXiv
Benkart, Georgia; Biswal, Rekha; Kirkman, Ellen; Van C. Nguyen; Zhu, Jieru McKay matrices for finite-dimensional Hopf algebras. (English) Zbl 1490.19001 Can. J. Math. 74, No. 3, 686-731 (2022). Reviewer: Mee Seong Im (Annapolis) MSC: 19A49 16T05 33C45 PDFBibTeX XMLCite \textit{G. Benkart} et al., Can. J. Math. 74, No. 3, 686--731 (2022; Zbl 1490.19001) Full Text: DOI arXiv
Dinkins, Hunter; Smirnov, Andrey Capped vertex with descendants for zero dimensional \(A_\infty\) quiver varieties. (English) Zbl 1492.14011 Adv. Math. 401, Article ID 108324, 30 p. (2022). Reviewer: Mee Seong Im (Annapolis) MSC: 14C35 16G20 19L47 33C80 39A70 16E20 14N99 33D52 PDFBibTeX XMLCite \textit{H. Dinkins} and \textit{A. Smirnov}, Adv. Math. 401, Article ID 108324, 30 p. (2022; Zbl 1492.14011) Full Text: DOI arXiv
Alarie-Vézina, L.; Lapointe, L.; Mathieu, P. The \(\mathcal{N}=2\) supersymmetric Calogero-Sutherland model and its eigenfunctions. (English) Zbl 1487.81161 Adv. Theor. Math. Phys. 25, No. 3, 543-590 (2021). MSC: 81V72 81Q60 16R50 81Q80 35L65 14D15 33C45 81P55 PDFBibTeX XMLCite \textit{L. Alarie-Vézina} et al., Adv. Theor. Math. Phys. 25, No. 3, 543--590 (2021; Zbl 1487.81161) 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
Groenevelt, Wolter A quantum algebra approach to multivariate Askey-Wilson polynomials. (English) Zbl 1470.81038 Int. Math. Res. Not. 2021, No. 5, 3224-3266 (2021). MSC: 81R50 17B37 17B45 16S10 33C45 62H12 14D21 PDFBibTeX XMLCite \textit{W. Groenevelt}, Int. Math. Res. Not. 2021, No. 5, 3224--3266 (2021; Zbl 1470.81038) Full Text: DOI arXiv
Koshida, Shinji Free field approach to the Macdonald process. (English) Zbl 1470.05166 J. Algebr. Comb. 54, No. 1, 223-263 (2021). MSC: 05E05 05A17 60B05 33D52 16T05 PDFBibTeX XMLCite \textit{S. Koshida}, J. Algebr. Comb. 54, No. 1, 223--263 (2021; Zbl 1470.05166) Full Text: DOI arXiv
Garbali, Alexandr; de Gier, Jan The \(R\)-matrix of the quantum toroidal algebra \(U_{q,t}(\overset{..}{gl}_1)\) in the Fock module. (English) Zbl 1476.17006 Commun. Math. Phys. 384, No. 3, 1971-2008 (2021). Reviewer: Stepan Moskaliuk (Kyiv) MSC: 17B37 16T20 33D52 81R12 PDFBibTeX XMLCite \textit{A. Garbali} and \textit{J. de Gier}, Commun. Math. Phys. 384, No. 3, 1971--2008 (2021; Zbl 1476.17006) Full Text: DOI arXiv
Etingof, Pavel; Klyuev, Daniil; Rains, Eric; Stryker, Douglas Twisted traces and positive forms on quantized Kleinian singularities of type A. (English) Zbl 1491.53093 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 029, 31 p. (2021). MSC: 53D50 33C47 16W70 PDFBibTeX XMLCite \textit{P. Etingof} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 029, 31 p. (2021; Zbl 1491.53093) Full Text: DOI arXiv
Huang, Hau-Wen The universal DAHA of type \((C^\vee_1,C_1)\) and Leonard triples. (English) Zbl 1480.16058 Commun. Algebra 49, No. 3, 1255-1273 (2021). MSC: 16S99 16G30 33D45 33D80 81R10 PDFBibTeX XMLCite \textit{H.-W. Huang}, Commun. Algebra 49, No. 3, 1255--1273 (2021; Zbl 1480.16058) Full Text: DOI arXiv
Khovanov, Mikhail; Sazdanovic, Radmila Diagrammatic categorification of the Chebyshev polynomials of the second kind. (English) Zbl 1480.16037 J. Pure Appl. Algebra 225, No. 6, Article ID 106592, 24 p. (2021). MSC: 16G99 16S99 18G10 33C45 PDFBibTeX XMLCite \textit{M. Khovanov} and \textit{R. Sazdanovic}, J. Pure Appl. Algebra 225, No. 6, Article ID 106592, 24 p. (2021; Zbl 1480.16037) Full Text: DOI arXiv
Shibukawa, Genki An explicit formula of powers of the \(2\times 2\) quantum matrices and its applications. arXiv:2112.15464 Preprint, arXiv:2112.15464 [math.RA] (2021). MSC: 16T20 33C45 81R50 BibTeX Cite \textit{G. Shibukawa}, ``An explicit formula of powers of the $2\times 2$ quantum matrices and its applications'', Preprint, arXiv:2112.15464 [math.RA] (2021) Full Text: arXiv OA License
Huang, Hau-Wen The space of Dunkl monogenics associated with \(\mathbb Z_2^3\) and the universal Bannai–Ito algebra. arXiv:2111.08421 Preprint, arXiv:2111.08421 [math.RT] (2021). MSC: 11E88 16D70 33D45 81Q05 BibTeX Cite \textit{H.-W. Huang}, ``The space of Dunkl monogenics associated with $\mathbb Z_2^3$ and the universal Bannai--Ito algebra'', Preprint, arXiv:2111.08421 [math.RT] (2021) Full Text: arXiv OA License
Huang, Si-Yao; Huang, Hau-Wen The universal additive DAHA of type \((C_1^\vee,C_1)\) and Leonard triples. arXiv:2107.14477 Preprint, arXiv:2107.14477 [math.RT] (2021). MSC: 16G30 33D45 33D80 81R10 81R12 BibTeX Cite \textit{S.-Y. Huang} and \textit{H.-W. Huang}, ``The universal additive DAHA of type $(C_1^\vee,C_1)$ and Leonard triples'', Preprint, arXiv:2107.14477 [math.RT] (2021) Full Text: arXiv OA License
Wen, Chia-Yi; Huang, Hau-Wen The Terwilliger algebra of the halved cube. arXiv:2109.02021 Preprint, arXiv:2109.02021 [math.CO] (2021). MSC: 05E30 16D70 33D45 BibTeX Cite \textit{C.-Y. Wen} and \textit{H.-W. Huang}, ``The Terwilliger algebra of the halved cube'', Preprint, arXiv:2109.02021 [math.CO] (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
Huang, Hau-Wen Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero. (English) Zbl 1465.16015 Lett. Math. Phys. 110, No. 9, 2519-2541 (2020). MSC: 16G30 33D45 PDFBibTeX XMLCite \textit{H.-W. Huang}, Lett. Math. Phys. 110, No. 9, 2519--2541 (2020; Zbl 1465.16015) Full Text: DOI arXiv
Carlsson, Erik; Gorsky, Eugene; Mellit, Anton The \(\mathbb{A}_{q,t}\) algebra and parabolic flag Hilbert schemes. (English) Zbl 1441.16045 Math. Ann. 376, No. 3-4, 1303-1336 (2020). MSC: 16W50 05E16 14C05 16E35 19G38 33C52 57K18 PDFBibTeX XMLCite \textit{E. Carlsson} et al., Math. Ann. 376, No. 3--4, 1303--1336 (2020; Zbl 1441.16045) Full Text: DOI arXiv
Ehrig, Michael; Tubbenhauer, Daniel Algebraic properties of zigzag algebras. (English) Zbl 1480.16028 Commun. Algebra 48, No. 1, 11-36 (2020). MSC: 16G10 05C50 16E05 16S37 33C45 PDFBibTeX XMLCite \textit{M. Ehrig} and \textit{D. Tubbenhauer}, Commun. Algebra 48, No. 1, 11--36 (2020; Zbl 1480.16028) Full Text: DOI arXiv
Baseilhac, Pascal; Crampé, Nicolas FRT presentation of classical Askey-Wilson algebras. (English) Zbl 1425.81059 Lett. Math. Phys. 109, No. 10, 2187-2207 (2019). MSC: 81R50 81R10 81U15 33D45 16T25 81Q80 PDFBibTeX XMLCite \textit{P. Baseilhac} and \textit{N. Crampé}, Lett. Math. Phys. 109, No. 10, 2187--2207 (2019; Zbl 1425.81059) 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
Lee, R. N.; Onishchenko, A. I. Toward an analytic perturbative solution for the ABJM quantum spectral curve. (English. Russian original) Zbl 1421.82006 Theor. Math. Phys. 198, No. 2, 256-270 (2019); translation from Teor. Mat. Fiz. 198, No. 2, 292-308 (2019). MSC: 82B20 16T25 39A60 33C45 81T13 81T60 PDFBibTeX XMLCite \textit{R. N. Lee} and \textit{A. I. Onishchenko}, Theor. Math. Phys. 198, No. 2, 256--270 (2019; Zbl 1421.82006); translation from Teor. Mat. Fiz. 198, No. 2, 292--308 (2019) Full Text: DOI arXiv
Mazzocco, Marta Embedding of the rank 1 DAHA into \(Mat(2,\mathbb{T}_q)\) and its automorphisms. (English) Zbl 1409.33015 Konno, Hitoshi (ed.) et al., Representation theory, special functions and Painvlevé equations – RIMS 2015. Proceedings of the international conference on the occasion of Masatoshi Noumi’s 60th birthday, RIMS, Kyoto, Japan, March 3–6, 2015. Tokyo: Mathematical Society of Japan (MSJ). Adv. Stud. Pure Math. 76, 449-468 (2018). MSC: 33D80 33D52 16T99 PDFBibTeX XMLCite \textit{M. Mazzocco}, Adv. Stud. Pure Math. 76, 449--468 (2018; Zbl 1409.33015) Full Text: DOI arXiv Euclid
Borinsky, Michael Graphs in perturbation theory. Algebraic structure and asymptotics. (English) Zbl 1444.81002 Springer Theses. Cham: Springer; Berlin: HU Berlin (Diss.) (ISBN 978-3-030-03540-2/hbk; 978-3-030-03541-9/ebook). xviii, 173 p. (2018). MSC: 81-02 81T18 81T15 16T05 42C10 41A60 81V10 05C90 00A79 PDFBibTeX XMLCite \textit{M. Borinsky}, Graphs in perturbation theory. Algebraic structure and asymptotics. Cham: Springer; Berlin: HU Berlin (Diss.) (2018; Zbl 1444.81002) Full Text: DOI arXiv
Kato, Syu Demazure character formula for semi-infinite flag varieties. (English) Zbl 1398.14053 Math. Ann. 371, No. 3-4, 1769-1801 (2018). Reviewer: Arvid Siqveland (Kongsberg) MSC: 14M15 17B10 33D52 14C35 19A22 16G99 43A40 PDFBibTeX XMLCite \textit{S. Kato}, Math. Ann. 371, No. 3--4, 1769--1801 (2018; Zbl 1398.14053) Full Text: DOI arXiv Link
Feigin, Evgeny; Makedonskyi, Ievgen; Orr, Daniel Generalized Weyl modules and nonsymmetric \(q\)-Whittaker functions. (English) Zbl 1468.33020 Adv. Math. 330, 997-1033 (2018). MSC: 33D52 33C67 16S30 17B10 PDFBibTeX XMLCite \textit{E. Feigin} et al., Adv. Math. 330, 997--1033 (2018; Zbl 1468.33020) Full Text: DOI arXiv
Zurrián, Ignacio The algebra of differential operators for a matrix weight: an ultraspherical example. (English) Zbl 1405.16033 Int. Math. Res. Not. 2017, No. 8, 2402-2430 (2017). MSC: 16S32 33D45 PDFBibTeX XMLCite \textit{I. Zurrián}, Int. Math. Res. Not. 2017, No. 8, 2402--2430 (2017; Zbl 1405.16033) Full Text: DOI arXiv Link
Feigin, Evgeny; Makedonskyi, Ievgen Weyl modules for \(\mathfrak{osp}(1, 2)\) and nonsymmetric Macdonald polynomials. (English) Zbl 1416.17013 Math. Res. Lett. 24, No. 3, 741-766 (2017). MSC: 17B65 33D52 16D80 PDFBibTeX XMLCite \textit{E. Feigin} and \textit{I. Makedonskyi}, Math. Res. Lett. 24, No. 3, 741--766 (2017; Zbl 1416.17013) Full Text: DOI arXiv
Escobar Ruiz, Mauricio A.; Miller, Willard jun.; Subag, Eyal Contractions of degenerate quadratic algebras, abstract and geometric. (English) Zbl 1381.22016 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 099, 32 p. (2017). MSC: 22E70 16G99 37J35 37K10 33C45 17B60 81R05 PDFBibTeX XMLCite \textit{M. A. Escobar Ruiz} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 099, 32 p. (2017; Zbl 1381.22016) 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
Erdmann, Karin Correction to: “Ext-finite modules for weakly symmetric algebras with radical cube zero”. (English) Zbl 1430.16012 J. Aust. Math. Soc. 102, No. 1, 161 (2017). MSC: 16E40 16G10 16E05 15A24 33C45 PDFBibTeX XMLCite \textit{K. Erdmann}, J. Aust. Math. Soc. 102, No. 1, 161 (2017; Zbl 1430.16012) Full Text: DOI
Erdmann, Karin Ext-finite modules for weakly symmetric algebras with radical cube zero. (English) Zbl 1373.16025 J. Aust. Math. Soc. 102, No. 1, 108-121 (2017). Reviewer: Constantin-Cosmin Todea (Cluj-Napoca) MSC: 16E40 16G10 16E05 15A24 33C45 PDFBibTeX XMLCite \textit{K. Erdmann}, J. Aust. Math. Soc. 102, No. 1, 108--121 (2017; Zbl 1373.16025) 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
Mesquita, T. Augusta; Maroni, P. Two-orthogonal polynomial sequences as eigenfunctions of a third-order differential operator. (English) Zbl 1346.42035 Mediterr. J. Math. 13, No. 2, 687-701 (2016). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 42C05 16R60 33C45 PDFBibTeX XMLCite \textit{T. A. Mesquita} and \textit{P. Maroni}, Mediterr. J. Math. 13, No. 2, 687--701 (2016; Zbl 1346.42035) Full Text: DOI
Heinonen, Robin; Kalnins, Ernest G.; Miller, Willard jun.; Subag, Eyal Structure relations and Darboux contractions for 2D 2nd order superintegrable systems. (English) Zbl 1317.22013 SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 043, 33 p. (2015). MSC: 22E70 16G99 37J35 37K10 33C45 17B60 PDFBibTeX XMLCite \textit{R. Heinonen} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 11, Paper 043, 33 p. (2015; Zbl 1317.22013) Full Text: DOI arXiv EMIS
Hilger, Stefan Orthogonal Polynomials appearing in SIE grid representations. arXiv:1504.01946 Preprint, arXiv:1504.01946 [math.CA] (2015). MSC: 33C45 16G20 BibTeX Cite \textit{S. Hilger}, ``Orthogonal Polynomials appearing in SIE grid representations'', Preprint, arXiv:1504.01946 [math.CA] (2015) Full Text: arXiv OA License
Bezrukavnikov, Roman; Finkelberg, Michael; Vologodsky, Vadim Wreath Macdonald polynomials and the categorical McKay correspondence. With an appendix by Vadim Vologodsky. (English) Zbl 1326.14037 Camb. J. Math. 2, No. 2, 163-190 (2014). MSC: 14F05 14E16 14J60 16S32 05E05 05E10 14C05 33D52 PDFBibTeX XMLCite \textit{R. Bezrukavnikov} et al., Camb. J. Math. 2, No. 2, 163--190 (2014; Zbl 1326.14037) Full Text: DOI arXiv
Kalnins, Ernest G.; Miller, W. jun. Quadratic algebra contractions and second-order superintegrable systems. (English) Zbl 1300.22013 Anal. Appl., Singap. 12, No. 5, 583-612 (2014). MSC: 22E70 16G99 37J35 37K10 33C45 17B60 PDFBibTeX XMLCite \textit{E. G. Kalnins} and \textit{W. Miller jun.}, Anal. Appl., Singap. 12, No. 5, 583--612 (2014; Zbl 1300.22013) 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
Miller, Willard; Li, Qiushi Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere. arXiv:1411.2112 Preprint, arXiv:1411.2112 [math-ph] (2014). MSC: 22E70 16G99 37J35 37K10 33C45 17B60 BibTeX Cite \textit{W. Miller} and \textit{Q. Li}, ``Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere'', Preprint, arXiv:1411.2112 [math-ph] (2014) Full Text: DOI arXiv OA License
Van Willigenburg, Stephanie Noncommutative irreducible characters of the symmetric group and noncommutative Schur functions. (English) Zbl 1290.05155 J. Comb. 4, No. 4, 403-418 (2013). MSC: 05E05 16T30 05E10 16T05 20B30 30C30 33D52 PDFBibTeX XMLCite \textit{S. Van Willigenburg}, J. Comb. 4, No. 4, 403--418 (2013; Zbl 1290.05155) Full Text: DOI arXiv
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
Novelli, Jean-Christophe; Tevlin, Lenny; Thibon, Jean-Yves On some noncommutative symmetric functions analogous to Hall-Littlewood and Macdonald polynomials. (English) Zbl 1268.05231 Int. J. Algebra Comput. 23, No. 4, 779-801 (2013). MSC: 05E05 16T30 42C05 PDFBibTeX XMLCite \textit{J.-C. Novelli} et al., Int. J. Algebra Comput. 23, No. 4, 779--801 (2013; Zbl 1268.05231) Full Text: DOI arXiv
Miller, Willard The theory of contractions of 2D 2nd order quantum superintegrable systems and its relation to the Askey scheme for hypergeometric orthogonal polynomials. arXiv:1310.2202 Preprint, arXiv:1310.2202 [math-ph] (2013). MSC: 22E70 16G99 37J35 37K10 33C45 17B60 BibTeX Cite \textit{W. Miller}, ``The theory of contractions of 2D 2nd order quantum superintegrable systems and its relation to the Askey scheme for hypergeometric orthogonal polynomials'', Preprint, arXiv:1310.2202 [math-ph] (2013) Full Text: DOI arXiv OA License
Olshanski, Grigori Laguerre and Meixner orthogonal bases in the algebra of symmetric functions. (English) Zbl 1257.33015 Int. Math. Res. Not. 2012, No. 16, 3615-3679 (2012). Reviewer: C. L. Parihar (Indore) MSC: 33C45 05E05 33D52 16E45 PDFBibTeX XMLCite \textit{G. Olshanski}, Int. Math. Res. Not. 2012, No. 16, 3615--3679 (2012; Zbl 1257.33015) Full Text: DOI arXiv
Dupont, Grégoire Cluster multiplication in regular components via generalized Chebyshev polynomials. (English) Zbl 1253.16012 Algebr. Represent. Theory 15, No. 3, 527-549 (2012). Reviewer: Ryan Kinser (Boston) MSC: 16G20 13F60 16G70 13B25 05E15 33C45 33C67 PDFBibTeX XMLCite \textit{G. Dupont}, Algebr. Represent. Theory 15, No. 3, 527--549 (2012; Zbl 1253.16012) 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
Erdmann, Karin; Schroll, Sibylle Chebyshev polynomials on symmetric matrices. (English) Zbl 1218.33009 Linear Algebra Appl. 434, No. 12, 2475-2496 (2011). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 15A24 16E40 16E99 14B07 PDFBibTeX XMLCite \textit{K. Erdmann} and \textit{S. Schroll}, Linear Algebra Appl. 434, No. 12, 2475--2496 (2011; Zbl 1218.33009) Full Text: DOI arXiv
Griffeth, Stephen Towards a combinatorial representation theory for the rational Cherednik algebra of type \(G(r,p,n)\). (English) Zbl 1227.05265 Proc. Edinb. Math. Soc., II. Ser. 53, No. 2, 419-445 (2010). MSC: 05E10 16G99 20F55 33C52 33C80 PDFBibTeX XMLCite \textit{S. Griffeth}, Proc. Edinb. Math. Soc., II. Ser. 53, No. 2, 419--445 (2010; Zbl 1227.05265) Full Text: DOI arXiv
Essen, Arno van den The Amazing Image Conjecture. arXiv:1006.5801 Preprint, arXiv:1006.5801 [math.AG] (2010). MSC: 14R15 14E05 16S32 33C45 BibTeX Cite \textit{A. van den Essen}, ``The Amazing Image Conjecture'', Preprint, arXiv:1006.5801 [math.AG] (2010) Full Text: arXiv OA License
Mallah, Omar; Karam, Jalal On commutative and nil-semiclean rings. (English) Zbl 1341.16037 Lagakos, Stephen (ed.) et al., Recent advances in applied mathematics. Proceedings of the American conference on applied mathematics (AMERICAN-MATH ’10), Harvard University, Cambridge, MA, USA, January 27–29, 2010. Athens: WSEAS Press (ISBN 978-960-474-150-2). Mathematics and Computers in Science and Engineering, 127-130 (2009). MSC: 16U60 16N40 16N20 16U80 13F20 PDFBibTeX XMLCite \textit{O. Mallah} and \textit{J. Karam}, in: Recent advances in applied mathematics. Proceedings of the American conference on applied mathematics (AMERICAN-MATH '10), Harvard University, Cambridge, MA, USA, January 27--29, 2010. Athens: WSEAS Press. 127--130 (2009; Zbl 1341.16037)
Feigin, B.; Hashizume, K.; Hoshino, Ayumu; Shiraishi, Jun’ichi; Yanagida, S. A commutative algebra on degenerate \(\mathbb{CP}^1\) and Macdonald polynomials. (English) Zbl 1248.33034 J. Math. Phys. 50, No. 9, 095215, 42 p. (2009). MSC: 33D80 33D52 16S80 16W50 PDFBibTeX XMLCite \textit{B. Feigin} et al., J. Math. Phys. 50, No. 9, 095215, 42 p. (2009; Zbl 1248.33034) Full Text: DOI arXiv
Brega, A. O.; Cagliero, L. R. LU-decomposition of a noncommutative linear system and Jacobi polynomials. (English) Zbl 1179.33009 J. Lie Theory 19, No. 3, 463-481 (2009). MSC: 33C45 22E46 33C05 16S30 PDFBibTeX XMLCite \textit{A. O. Brega} and \textit{L. R. Cagliero}, J. Lie Theory 19, No. 3, 463--481 (2009; Zbl 1179.33009) Full Text: arXiv Link
Nagao, Kentaro \(K\)-theory of quiver varieties, \(q\)-Fock space and nonsymmetric Macdonald polynomials. (English) Zbl 1246.17020 Osaka J. Math. 46, No. 3, 877-907 (2009). Reviewer: Justyna Kosakowska (Toruń) MSC: 17B37 33C52 14D21 16G20 PDFBibTeX XMLCite \textit{K. Nagao}, Osaka J. Math. 46, No. 3, 877--907 (2009; Zbl 1246.17020) Full Text: arXiv Euclid
Konno, Hitoshi Elliptic quantum group \(U_{q,p}(\widehat{\mathfrak{sl}}_2)\), Hopf algebroid structure and elliptic hypergeometric series. (English) Zbl 1210.17023 J. Geom. Phys. 59, No. 11, 1485-1511 (2009). Reviewer: Jan Grabowski (Oxford) MSC: 17B37 17B69 81R50 16T15 33C45 PDFBibTeX XMLCite \textit{H. Konno}, J. Geom. Phys. 59, No. 11, 1485--1511 (2009; Zbl 1210.17023) Full Text: DOI arXiv
Humphries, Stephen P. Intersection theories and Chebyshev polynomials. III. (English) Zbl 1243.57012 J. Algebra Appl. 8, No. 1, 53-81 (2009). MSC: 57M50 11T06 16S99 33C45 PDFBibTeX XMLCite \textit{S. P. Humphries}, J. Algebra Appl. 8, No. 1, 53--81 (2009; Zbl 1243.57012) Full Text: DOI
Stan, Aurel I. A characterization of probability measures in terms of Wick product inequalities. (English) Zbl 1160.33008 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 3, 377-391 (2008). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 46H25 46N30 16W50 60E15 PDFBibTeX XMLCite \textit{A. I. Stan}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, No. 3, 377--391 (2008; Zbl 1160.33008) Full Text: DOI
Castro, Mirta M.; Grünbaum, F. Alberto The noncommutative bispectral problem for operators of order one. (English) Zbl 1157.39001 Constr. Approx. 27, No. 3, 329-347 (2008). Reviewer: Roman Šimon Hilscher (Brno) MSC: 39A10 47B36 15A24 16S32 34L40 42C05 PDFBibTeX XMLCite \textit{M. M. Castro} and \textit{F. A. Grünbaum}, Constr. Approx. 27, No. 3, 329--347 (2008; Zbl 1157.39001) Full Text: DOI
Ito, Tatsuro; Terwilliger, Paul The \(q\)-tetrahedron algebra and its finite dimensional irreducible modules. (English) Zbl 1133.17011 Commun. Algebra 35, No. 11, 3415-3439 (2007). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 17B37 16W35 05E35 82B23 PDFBibTeX XMLCite \textit{T. Ito} and \textit{P. Terwilliger}, Commun. Algebra 35, No. 11, 3415--3439 (2007; Zbl 1133.17011) Full Text: DOI arXiv
Ito, Tatsuro; Terwilliger, Paul \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra. (English) Zbl 1146.17009 Linear Algebra Appl. 426, No. 2-3, 516-532 (2007). MSC: 17B37 05E35 16G10 16W35 82B23 PDFBibTeX XMLCite \textit{T. Ito} and \textit{P. Terwilliger}, Linear Algebra Appl. 426, No. 2--3, 516--532 (2007; Zbl 1146.17009) Full Text: DOI arXiv
Ito, Tatsuro; Terwilliger, Paul Two non-nilpotent linear transformations that satisfy the cubic \(q\)-Serre relations. (English) Zbl 1179.17017 J. Algebra Appl. 6, No. 3, 477-503 (2007). MSC: 17B37 16T20 05E30 33D45 33D80 PDFBibTeX XMLCite \textit{T. Ito} and \textit{P. Terwilliger}, J. Algebra Appl. 6, No. 3, 477--503 (2007; Zbl 1179.17017) Full Text: DOI arXiv
Ito, Tatsuro; Terwilliger, Paul Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\). (English) Zbl 1128.16028 Ramanujan J. 13, No. 1-3, 39-62 (2007). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 16W35 17B37 33D80 33D45 PDFBibTeX XMLCite \textit{T. Ito} and \textit{P. Terwilliger}, Ramanujan J. 13, No. 1--3, 39--62 (2007; Zbl 1128.16028) Full Text: DOI arXiv
Hetyei, Gábor Central Delannoy numbers and balanced Cohen-Macaulay complexes. (English) Zbl 1116.13017 Ann. Comb. 10, No. 4, 443-462 (2006). Reviewer: Marius Tarnauceanu (Iaşi) MSC: 13F55 05A15 16E65 33C45 PDFBibTeX XMLCite \textit{G. Hetyei}, Ann. Comb. 10, No. 4, 443--462 (2006; Zbl 1116.13017) Full Text: DOI
Arvesú, Jorge Quantum algebras \(\text{SU}_q(2)\) and \(\text{SU}_q(1,1)\) associated with certain \(q\)-Hahn polynomials: a revisited approach. (English) Zbl 1109.33026 ETNA, Electron. Trans. Numer. Anal. 24, 24-44 (2006). MSC: 33D80 16W35 33D45 81R50 PDFBibTeX XMLCite \textit{J. Arvesú}, ETNA, Electron. Trans. Numer. Anal. 24, 24--44 (2006; Zbl 1109.33026) Full Text: EuDML Link
Atakishiyev, M. N.; Groza, V. A. The quantum algebra \(U_q(su_2)\) and \(q\)-Krawtchouk families of polynomials. (English) Zbl 1069.33018 J. Phys. A, Math. Gen. 37, No. 7, 2625-2635 (2004). MSC: 33D45 17B37 17B81 33D80 81R50 16W30 PDFBibTeX XMLCite \textit{M. N. Atakishiyev} and \textit{V. A. Groza}, J. Phys. A, Math. Gen. 37, No. 7, 2625--2635 (2004; Zbl 1069.33018) Full Text: DOI
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U. Big \(q\)-Laguerre and \(q\)-Meixner polynomials and representations of the quantum algebra \(U_q(su_{1,1}\)). (English) Zbl 1058.81040 J. Phys. A, Math. Gen. 36, No. 41, 10335-10347 (2003). MSC: 81R50 33C45 81R15 17B37 16W30 PDFBibTeX XMLCite \textit{M. N. Atakishiyev} et al., J. Phys. A, Math. Gen. 36, No. 41, 10335--10347 (2003; Zbl 1058.81040) Full Text: DOI arXiv
Gnatowska, Ewa; Strasburger, Aleksander The Weyl algebra, spherical harmonics, and Hahn polynomials. (English) Zbl 1023.81015 Strasburger, Aleksander (ed.) et al., Geometry and analysis on finite- and infinite-dimensional Lie groups. Proceedings of the workshop on Lie groups and Lie algebras, Bȩdlewo, Poland, September 4-15, 2000. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 55, 309-322 (2002). Reviewer: Joris Van der Jeugt (Gent) MSC: 81R10 81V70 33C45 33C80 33C55 16W25 PDFBibTeX XMLCite \textit{E. Gnatowska} and \textit{A. Strasburger}, Banach Cent. Publ. 55, 309--322 (2002; Zbl 1023.81015) Full Text: arXiv Link
Terwilliger, Paul Two relations that generalize the \(q\)-Serre relations and the Dolan-Grady relations. (English) Zbl 1061.16033 Kirillov, Anatol N. (ed.) et al., Physics and combinatorics. Proceedings of the international workshop, Nagoya, Japan, August 23–27, 1999. Singapore: World Scientific (ISBN 981-02-4578-5). 377-398 (2001). MSC: 16S15 16G30 33D45 05E35 05E30 81R50 PDFBibTeX XMLCite \textit{P. Terwilliger}, in: Physics and combinatorics. Proceedings of the international workshop, Nagoya, Japan, August 23--27, 1999. Singapore: World Scientific. 377--398 (2001; Zbl 1061.16033) Full Text: DOI arXiv
Floris, Paul G. A. Addition theorems for spherical polynomials on a family of quantum spheres. (English) Zbl 0938.33009 van Diejen, Jan Felipe (ed.) et al., Algebraic methods and \(q\)-special functions. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 22, 145-170 (1999). Reviewer: J.Saurer (Regensburg) MSC: 33D45 33D80 16W30 17B37 81R50 PDFBibTeX XMLCite \textit{P. G. A. Floris}, in: Algebraic methods and \(q\)-special functions. Providence,~RI: American Mathematical Society. 145--170 (1999; Zbl 0938.33009)
Bultheel, Adhemar; Van Barel, Marc Linear algebra, rational approximation and orthogonal polynomials. (English) Zbl 0890.65024 Studies in Computational Mathematics. 6. Amsterdam: North-Holland. 446 p. (1997). Reviewer: W.Gander (Zürich) MSC: 65Fxx 65-02 41-02 15-02 41A20 41A21 42C05 11A05 16W60 15B57 40A20 65T50 44A60 PDFBibTeX XMLCite \textit{A. Bultheel} and \textit{M. Van Barel}, Linear algebra, rational approximation and orthogonal polynomials. Amsterdam: North-Holland (1997; Zbl 0890.65024)
Floris, Paul G. A. Addition formula for \(q\)-disk polynomials. (English) Zbl 0891.33009 Compos. Math. 108, No. 2, 123-149 (1997). MSC: 33D45 33D80 81R50 17B37 16W30 PDFBibTeX XMLCite \textit{P. G. A. Floris}, Compos. Math. 108, No. 2, 123--149 (1997; Zbl 0891.33009) Full Text: DOI arXiv
Koornwinder, Tom H. Compact quantum groups and \(q\)-special functions. (English) Zbl 0821.17015 Baldoni, Velleda (ed.) et al., Representations of Lie groups and quantum groups. Proceedings of the session of the European School of Group Theory, held in Trento, Italy, July 19-30, 1993. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 311, 46-128 (1994). Reviewer: A.Klimyk (Kiev) MSC: 17B37 16W30 33D15 33D45 46L89 PDFBibTeX XMLCite \textit{T. H. Koornwinder}, Pitman Res. Notes Math. Ser. 311, 46--128 (1994; Zbl 0821.17015)
Koelink, H. T. The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function. (English) Zbl 0814.33011 Duke Math. J. 76, No. 2, 483-508 (1994). Reviewer: H.Exton (Dunrossness) MSC: 33D15 33D45 33D80 17B37 16W30 PDFBibTeX XMLCite \textit{H. T. Koelink}, Duke Math. J. 76, No. 2, 483--508 (1994; Zbl 0814.33011) Full Text: DOI
Floreanini, Roberto; Vinet, Luc \(q\)-orthogonal polynomials and the oscillator quantum group. (English) Zbl 0745.33008 Lett. Math. Phys. 22, No. 1, 45-54 (1991). MSC: 33D80 17B37 16W30 33D45 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, Lett. Math. Phys. 22, No. 1, 45--54 (1991; Zbl 0745.33008) Full Text: DOI
Masuda, Tetsuya; Mimachi, Katsuhisa; Nakagami, Yoshiomi; Noumi, Masatoshi; Ueno, Kimio Representations of quantum groups and a q-analogue of orthogonal polynomials. (Représentations des groupes quantiques et un q-analogue des polynômes orthogonaux). (English) Zbl 0658.22010 C. R. Acad. Sci., Paris, Sér. I 307, No. 11, 559-564 (1988). Reviewer: G.Loupias MSC: 22E70 81R10 58H05 16W30 33C80 PDFBibTeX XMLCite \textit{T. Masuda} et al., C. R. Acad. Sci., Paris, Sér. I 307, No. 11, 559--564 (1988; Zbl 0658.22010)
Jacobson, Nathan Basic algebra I. 2nd ed. (English) Zbl 0557.16001 New York: W. H. Freeman and Company. XVIII, 499 p. £19.95 (1985). Reviewer: B.Richter MSC: 16-01 12-01 13-01 20-01 00A05 06-01 15-01 PDFBibTeX XML
Krempa, J.; Matczuk, J. On algebraic derivations of prime rings. (English) Zbl 0552.16017 Methods in ring theory, Proc. NATO Adv. Study Inst., Antwerp/Belg. 1983, NATO ASI Ser., Ser. C 129, 211-229 (1984). Reviewer: H.E.Bell MSC: 16W20 16N60 16U99 PDFBibTeX XML
Kirkwood, B.; McDonald, B. R. The Witt ring of a full ring. (English) Zbl 0438.13001 J. Algebra 64, 148-166 (1980). MSC: 13A05 16E50 20H25 13H99 13B25 PDFBibTeX XMLCite \textit{B. Kirkwood} and \textit{B. R. McDonald}, J. Algebra 64, 148--166 (1980; Zbl 0438.13001) Full Text: DOI
Lenormand, Claude Polynômes classiques en variables non commutatives. (French) Zbl 0469.16003 Series formelles en variables non commutatives et applications, Actes 5ieme Ec. de Printemps d’Inf. theor., Vieux-Boucau les Bains 1977, 181-207 (1978). MSC: 16S10 16W60 16W20 05A19 33C55 33C45 PDFBibTeX XML