Dunkl, Charles F. The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions. (English) Zbl 07735305 J. Phys. A, Math. Theor. 56, No. 37, Article ID 375301, 23 p. (2023). MSC: 81R05 70H05 35J05 20F55 20B30 22E70 17B22 05A15 28C20 42C05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, J. Phys. A, Math. Theor. 56, No. 37, Article ID 375301, 23 p. (2023; Zbl 07735305) Full Text: DOI arXiv
Dunkl, Charles F. The \(B_2\) harmonic oscillator with reflections and superintegrability. (English) Zbl 1515.81141 SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 025, 18 p. (2023). MSC: 81R12 37J35 33C45 81Q05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 19, Paper 025, 18 p. (2023; Zbl 1515.81141) Full Text: DOI arXiv
Dunkl, Charles F. A superpolynomial version of nonsymmetric Jack polynomials. (English) Zbl 1518.33008 Ramanujan J. 61, No. 1, 203-236 (2023). Reviewer: Francisco Marcellán (Leganes) MSC: 33C52 20C30 17A70 81Q80 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Ramanujan J. 61, No. 1, 203--236 (2023; Zbl 1518.33008) Full Text: DOI arXiv
Colmenarejo, Laura; Dunkl, Charles F.; Luque, Jean-Gabriel Connections between vector-valued and highest weight Jack and Macdonald polynomials. (English) Zbl 1517.33007 Ann. Inst. Henri Poincaré D, Comb. Phys. Interact. 9, No. 2, 297-348 (2022). MSC: 33D52 05E05 05E10 20C08 20C30 81V70 PDFBibTeX XMLCite \textit{L. Colmenarejo} et al., Ann. Inst. Henri Poincaré D, Comb. Phys. Interact. 9, No. 2, 297--348 (2022; Zbl 1517.33007) Full Text: DOI arXiv
Dunkl, Charles F. The Classification of All Singular Nonsymmetric Macdonald Polynomials. arXiv:2111.13618 Preprint, arXiv:2111.13618 [math.RT] (2021). MSC: 33D52 20C08 05E10 BibTeX Cite \textit{C. F. Dunkl}, ``The Classification of All Singular Nonsymmetric Macdonald Polynomials'', Preprint, arXiv:2111.13618 [math.RT] (2021) Full Text: arXiv OA License
Dunkl, Charles F. Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points. arXiv:2104.00710 Preprint, arXiv:2104.00710 [math.CO] (2021). MSC: 33D52 20C08 05E05 BibTeX Cite \textit{C. F. Dunkl}, ``Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points'', Preprint, arXiv:2104.00710 [math.CO] (2021) Full Text: DOI arXiv OA License
Colmenarejo, Laura; Dunkl, Charles F. Singular nonsymmetric Macdonald polynomials and quasistaircases. (English) Zbl 1435.33021 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 010, 27 p. (2020). MSC: 33D52 05E10 20C08 33D80 PDFBibTeX XMLCite \textit{L. Colmenarejo} and \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 010, 27 p. (2020; Zbl 1435.33021) Full Text: DOI arXiv
Dunkl, Charles F. Singular nonsymmetric Jack polynomials for some rectangular tableaux. arXiv:2003.01646 Preprint, arXiv:2003.01646 [math.RT] (2020). MSC: 20C30 33C52 05E10 BibTeX Cite \textit{C. F. Dunkl}, ``Singular nonsymmetric Jack polynomials for some rectangular tableaux'', Preprint, arXiv:2003.01646 [math.RT] (2020) Full Text: arXiv OA License
Dunkl, Charles F. Some singular vector-valued Jack and Macdonald polynomials. (English) Zbl 1425.33007 Symmetry 11, No. 4, Paper No. 503, 14 p. (2019). MSC: 33C52 33D52 05E10 20C08 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Symmetry 11, No. 4, Paper No. 503, 14 p. (2019; Zbl 1425.33007) Full Text: DOI arXiv
Dunkl, Charles F. The smallest singular values and vector-valued Jack polynomials. (English) Zbl 1401.33010 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 115, 20 p. (2018). MSC: 33C52 05E10 05E05 20F55 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 115, 20 p. (2018; Zbl 1401.33010) Full Text: DOI arXiv
Ciarlet, Patrick jun.; Dunkl, Charles F.; Sauter, Stefan A. A family of Crouzeix-Raviart finite elements in 3D. (English) Zbl 1396.33020 Anal. Appl., Singap. 16, No. 5, 649-691 (2018). MSC: 33C45 33C50 33C80 65N12 65N30 PDFBibTeX XMLCite \textit{P. Ciarlet jun.} et al., Anal. Appl., Singap. 16, No. 5, 649--691 (2018; Zbl 1396.33020) Full Text: DOI arXiv
Dunkl, Charles F. The smallest singular values of the icosahedral group. arXiv:1809.02107 Preprint, arXiv:1809.02107 [math.RT] (2018). MSC: 33C52 20F55 33C80 BibTeX Cite \textit{C. F. Dunkl}, ``The smallest singular values of the icosahedral group'', Preprint, arXiv:1809.02107 [math.RT] (2018) Full Text: arXiv OA License
Dunkl, Charles F. Vector-valued Jack polynomials and wavefunctions on the torus. (English) Zbl 1369.81031 J. Phys. A, Math. Theor. 50, No. 24, Article ID 245201, 21 p. (2017). MSC: 81Q10 81V70 20C30 14M25 33C50 81Q35 81S05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, J. Phys. A, Math. Theor. 50, No. 24, Article ID 245201, 21 p. (2017; Zbl 1369.81031) Full Text: DOI arXiv
Dunkl, Charles F. A linear system of differential equations related to vector-valued Jack polynomials on the torus. (English) Zbl 1366.33008 SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 040, 41 p. (2017). MSC: 33C52 20C30 32W50 35F35 42B05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 13, Paper 040, 41 p. (2017; Zbl 1366.33008) Full Text: DOI arXiv
Dunkl, Charles F. Orthogonality measure on the torus for vector-valued Jack polynomials. (English) Zbl 1338.33024 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 033, 27 p. (2016). MSC: 33C52 42B10 20C30 46G10 35F35 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 033, 27 p. (2016; Zbl 1338.33024) Full Text: DOI arXiv
Dunkl, Charles F.; Luque, Jean-Gabriel Clustering properties of rectangular Macdonald polynomials. (English) Zbl 1322.05133 Ann. Inst. Henri Poincaré D, Comb. Phys. Interact. 2, No. 3, 263-307 (2015). MSC: 05E05 20C35 33D52 81V70 05E10 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{J.-G. Luque}, Ann. Inst. Henri Poincaré D, Comb. Phys. Interact. 2, No. 3, 263--307 (2015; Zbl 1322.05133) Full Text: DOI arXiv
Dunkl, Charles F.; Xu, Yuan Orthogonal polynomials of several variables. 2nd ed. (English) Zbl 1317.33001 Encyclopedia of Mathematics and Its Applications 155. Cambridge: Cambridge University Press (ISBN 978-1-107-07189-6/hbk; 978-1-107-78613-4/ebook). xvii, 420 p. (2014). Reviewer: Bujar Fejzullahu (Presevo) MSC: 33-02 33C50 33C45 20F55 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{Y. Xu}, Orthogonal polynomials of several variables. 2nd ed. Cambridge: Cambridge University Press (2014; Zbl 1317.33001) Full Text: DOI
Dunkl, Charles F. Vector polynomials and a matrix weight associated to dihedral groups. (English) Zbl 1293.33016 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 044, 23 p. (2014). MSC: 33C52 20F55 33C45 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 044, 23 p. (2014; Zbl 1293.33016) Full Text: DOI arXiv EMIS
Dunkl, Charles F. Vector-valued polynomials and a matrix weight function with \(B_{2}\)-action. II. (English) Zbl 1272.33015 SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 043, 11 p. (2013). MSC: 33C52 33C20 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 043, 11 p. (2013; Zbl 1272.33015) Full Text: DOI arXiv
Dunkl, Charles F. Vector-valued polynomials and a matrix weight function with \(B_{2}\)-action. (English) Zbl 1272.33014 SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 007, 23 p. (2013). MSC: 33C52 42C05 33C05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 9, Paper 007, 23 p. (2013; Zbl 1272.33014) Full Text: DOI arXiv
Dunkl, Charles F. Dunkl Operators and Related Special Functions. arXiv:1210.3010 Preprint, arXiv:1210.3010 [math.CA] (2012). MSC: 33C52 20F55 BibTeX Cite \textit{C. F. Dunkl}, ``Dunkl Operators and Related Special Functions'', Preprint, arXiv:1210.3010 [math.CA] (2012) Full Text: arXiv OA License
Dunkl, Charles F. Reflection groups in analysis and applications. (English) Zbl 1191.33006 Jpn. J. Math. (3) 3, No. 2, 215-246 (2008). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C52 20F55 33D80 42C05 81R12 05E05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Jpn. J. Math. (3) 3, No. 2, 215--246 (2008; Zbl 1191.33006) Full Text: DOI
Dunkl, Charles F. Some orthogonal polynomials in four variables. (English) Zbl 1163.33310 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 082, 9 p. (2008). MSC: 33C52 05E35 37J35 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 082, 9 p. (2008; Zbl 1163.33310) Full Text: DOI arXiv EuDML
Dunkl, Charles F. Polynomials associated with dihedral groups. (English) Zbl 1132.33005 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 052, 19 p. (2007). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 33C80 20F55 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 052, 19 p. (2007; Zbl 1132.33005) Full Text: DOI arXiv EuDML EMIS
Dunkl, Charles F. Hook-lengths and pairs of compositions. (English) Zbl 1155.05060 J. Comput. Appl. Math. 199, No. 1, 39-47 (2007). MSC: 05E10 05E35 33C52 PDFBibTeX XMLCite \textit{C. F. Dunkl}, J. Comput. Appl. Math. 199, No. 1, 39--47 (2007; Zbl 1155.05060) Full Text: DOI arXiv
Dunkl, Charles F. Singular polynomials and modules for the symmetric groups. (English) Zbl 1102.33012 Int. Math. Res. Not. 2005, No. 39, 2409-2436 (2005). Reviewer: Margit Roesler (Clausthal-Zellerfeld) MSC: 33C52 05E10 20C30 33C67 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Int. Math. Res. Not. 2005, No. 39, 2409--2436 (2005; Zbl 1102.33012) Full Text: DOI arXiv
Dunkl, Charles F. Singular polynomials for the symmetric groups. (English) Zbl 1078.33017 Int. Math. Res. Not. 2004, No. 67, 3607-3635 (2004). Reviewer: Giovanna Carnovale (Padova) MSC: 33D52 05E10 20C30 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Int. Math. Res. Not. 2004, No. 67, 3607--3635 (2004; Zbl 1078.33017) Full Text: DOI arXiv
Dunkl, Charles F. A Laguerre polynomial orthogonality and the hydrogen atom. (English) Zbl 1047.33003 Anal. Appl., Singap. 1, No. 2, 177-188 (2003). Reviewer: Aleksey A. Dovgoshey (Donetsk) MSC: 33C45 33C15 35Q40 81V45 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Anal. Appl., Singap. 1, No. 2, 177--188 (2003; Zbl 1047.33003) Full Text: DOI arXiv
Dunkl, C. F.; Opdam, E. M. Dunkl operators for complex reflection groups. (English) Zbl 1042.20025 Proc. Lond. Math. Soc., III. Ser. 86, No. 1, 70-108 (2003). Reviewer: Chen Chengdong (Shanghai) MSC: 20F55 05E05 18G35 33C52 33C80 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{E. M. Opdam}, Proc. Lond. Math. Soc. (3) 86, No. 1, 70--108 (2003; Zbl 1042.20025) Full Text: DOI arXiv
Dunkl, Charles F. Special functions and generating functions associated with reflection groups. (English) Zbl 1041.33011 J. Comput. Appl. Math. 153, No. 1-2, 181-190 (2003). Reviewer: Ajendra Nath Srivastava (Puna) MSC: 33C80 33C50 05E05 81V70 PDFBibTeX XMLCite \textit{C. F. Dunkl}, J. Comput. Appl. Math. 153, No. 1--2, 181--190 (2003; Zbl 1041.33011) Full Text: DOI
Dunkl, Charles F. Orthogonal polynomials and reflection groups. (English) Zbl 0997.33005 Bustoz, Joaquin (ed.) et al., Special functions 2000: current perspective and future directions. Proceedings of the NATO Advanced Study Institute, Tempe, AZ, USA, May 29-June 9, 2000. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 30, 111-128 (2001). Reviewer: Angela Pasquale (Clausthal-Zellerfeld) MSC: 33C52 33C80 PDFBibTeX XMLCite \textit{C. F. Dunkl}, NATO Sci. Ser. II, Math. Phys. Chem. 30, 111--128 (2001; Zbl 0997.33005)
Dunkl, Charles F.; Xu, Yuan Orthogonal polynomials of several variables. (English) Zbl 0964.33001 Encyclopedia of Mathematics and Its Applications. 81. Cambridge: Cambridge University Press. xv, 390 p. (2001). Reviewer: A.Klimyk (Kyïv) MSC: 33-02 33C50 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{Y. Xu}, Orthogonal polynomials of several variables. Cambridge: Cambridge University Press (2001; Zbl 0964.33001)
Dunkl, Charles F. Generating functions associated with dihedral groups. (English) Zbl 1097.33504 Dunkl, Charles (ed.) et al., Special functions. Proceedings of the international workshop on special functions – asymptotics, harmonic analysis and mathematical physics, Hong Kong, China, June 21–25, 1999. Singapore: World Scientific (ISBN 981-02-4393-6/hbk). 72-87 (2000). MSC: 33C45 05A15 20F55 33C80 PDFBibTeX XMLCite \textit{C. F. Dunkl}, in: Special functions. Proceedings of the international workshop on special functions -- asymptotics, harmonic analysis and mathematical physics, Hong Kong, China, June 21--25, 1999. Singapore: World Scientific. 72--87 (2000; Zbl 1097.33504) Full Text: DOI
Dunkl, Charles F. Computing with differential-difference operators. (English) Zbl 0946.65009 J. Symb. Comput. 28, No. 6, 819-826 (1999). Reviewer: D.Petcu (Timişoara) MSC: 65D20 33C80 33C45 33F10 68W30 PDFBibTeX XMLCite \textit{C. F. Dunkl}, J. Symb. Comput. 28, No. 6, 819--826 (1999; Zbl 0946.65009) Full Text: DOI
Dunkl, Charles F. Orthogonal polynomials of types \(A\) and \(B\) and related Calogero models. (English) Zbl 0936.33006 Commun. Math. Phys. 197, No. 2, 451-487 (1998). Reviewer: D.M.Bressoud (St.Paul) MSC: 33C80 81V70 33C45 33-02 81U15 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Commun. Math. Phys. 197, No. 2, 451--487 (1998; Zbl 0936.33006) Full Text: DOI arXiv
Dunkl, Charles F.; Hanlon, Phil Integrals of polynomials associated with tableaux and the Garsia-Haiman conjecture. (English) Zbl 1018.05106 Math. Z. 228, No. 3, 537-567 (1998). MSC: 05E10 20C30 33D52 17B05 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{P. Hanlon}, Math. Z. 228, No. 3, 537--567 (1998; Zbl 1018.05106) Full Text: DOI
Dunkl, Charles F. Harmonic polynomials and peak sets of reflection groups. (English) Zbl 0685.33012 Geom. Dedicata 32, No. 2, 157-171 (1989). Reviewer: Ch.F.Dunkl MSC: 33C45 20H15 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Geom. Dedicata 32, No. 2, 157--171 (1989; Zbl 0685.33012) Full Text: DOI
Dunkl, Charles F. Differential-difference operators associated to reflection groups. (English) Zbl 0652.33004 Trans. Am. Math. Soc. 311, No. 1, 167-183 (1989). MSC: 33C55 33C45 20F55 42C10 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Trans. Am. Math. Soc. 311, No. 1, 167--183 (1989; Zbl 0652.33004) Full Text: DOI
Dunkl, Charles F. Reflection groups and orthogonal polynomials on the sphere. (English) Zbl 0616.33005 Math. Z. 197, No. 1, 33-60 (1988). MSC: 33C55 33C45 20B25 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Math. Z. 197, No. 1, 33--60 (1988; Zbl 0616.33005) Full Text: DOI EuDML
Dunkl, Charles F. Orthogonal polynomials on the hexagon. (English) Zbl 0613.33010 SIAM J. Appl. Math. 47, 343-351 (1987). MSC: 33C45 20H15 41A10 78A55 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIAM J. Appl. Math. 47, 343--351 (1987; Zbl 0613.33010) Full Text: DOI
Dunkl, Charles F. Orthogonal polynomials and a Dirichlet problem related to the Hilbert transform. (English) Zbl 0589.31004 Indag. Math. 47, 147-171 (1985). Reviewer: D.H.Armitage MSC: 31A25 33C45 43A99 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Indag. Math. 47, 147--171 (1985; Zbl 0589.31004)
Dunkl, Charles F. Orthogonal polynomials with symmetry of order three. (English) Zbl 0559.33005 Can. J. Math. 36, 685-717 (1984). MSC: 33C45 33C55 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Can. J. Math. 36, 685--717 (1984; Zbl 0559.33005) Full Text: DOI
Dunkl, Charles F. Orthogonal polynomials on the sphere with octahedral symmetry. (English) Zbl 0541.33002 Trans. Am. Math. Soc. 282, 555-575 (1984). MSC: 33C55 33C45 20H15 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Trans. Am. Math. Soc. 282, 555--575 (1984; Zbl 0541.33002) Full Text: DOI
Dunkl, Charles F. The Poisson kernel for Heisenberg polynomials on the disk. (English) Zbl 0538.43005 Math. Z. 187, 527-547 (1984). MSC: 43A80 22E30 33C55 42C10 33C45 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Math. Z. 187, 527--547 (1984; Zbl 0538.43005) Full Text: DOI EuDML
Dunkl, Charles F. A difference equation and Hahn polynomials in two variables. (English) Zbl 0459.33007 Pac. J. Math. 92, 57-71 (1981). MSC: 33C05 33C45 39A05 20C30 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Pac. J. Math. 92, 57--71 (1981; Zbl 0459.33007) Full Text: DOI
Dunkl, Charles F. Orthogonal polynomials in two variables of q-Hahn and q-Jacobi type. (English) Zbl 0499.33007 SIAM J. Algebraic Discrete Methods 1, 137-157 (1980). MSC: 33C45 33C05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIAM J. Algebraic Discrete Methods 1, 137--157 (1980; Zbl 0499.33007) Full Text: DOI
Dunkl, Charles F. Discrete quadrature and bounds on t-designs. (English) Zbl 0407.05021 Mich. Math. J. 26, 81-102 (1979). MSC: 05B30 33C45 41A55 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Mich. Math. J. 26, 81--102 (1979; Zbl 0407.05021) Full Text: DOI
Dunkl, Charles F. Orthogonal functions on some permutation groups. (English) Zbl 0404.20005 Relations between combinatorics and other parts of mathematics, Proc. Symp. Pure Math. Am. Math. Soc., Columbus, Ohio 1978, Proc. Symp. Pure Math. 34, 129-147 (1979). MSC: 20C30 20C15 20G05 20G40 05C99 05B30 PDFBibTeX XML
Dunkl, Charles F. An addition theorem for some q-Hahn polynomials. (English) Zbl 0345.33010 Monatsh. Math. 85, 5-37 (1978). MSC: 33C55 43A85 42C10 20G05 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Monatsh. Math. 85, 5--37 (1978; Zbl 0345.33010) Full Text: DOI EuDML
Dunkl, Charles F. A Krawtchouk polynomial addition theorem and wreath products of symmetric groups. (English) Zbl 0326.33008 Indiana Univ. Math. J. 25, 335-358 (1976). MSC: 33C45 33C55 20C30 43A75 PDFBibTeX XMLCite \textit{C. F. Dunkl}, Indiana Univ. Math. J. 25, 335--358 (1976; Zbl 0326.33008) Full Text: DOI
Dunkl, Charles F. A n expansion in ultraspherical polynomials with nonnegative coefficients. (English) Zbl 0308.42011 SIAM J. Math. Anal. 5, 51-52 (1974). MSC: 42C15 33C45 42C05 43A90 PDFBibTeX XMLCite \textit{C. F. Dunkl}, SIAM J. Math. Anal. 5, 51--52 (1974; Zbl 0308.42011) Full Text: DOI