Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group. (English) Zbl 1064.33009
Summary: Some classes of orthogonal polynomials are discussed in this paper which are expressed in terms of \((n+1,m+1)\)-hypergeometric functions. The orthogonality comes from that of zonal spherical functions of certain Gelfand pairs.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 05E35 | Orthogonal polynomials (combinatorics) (MSC2000) |
| 05E05 | Symmetric functions and generalizations |
Keywords:
Discrete orthogonal polynomials; \((n+1,m+1)\)-hypergeometric functions; Gelfand pair of finite groups; Zonal spherical functionsReferences:
| [1] | Aomoto, K.; Kita, M., Theory of Hypergeometric Functions (1994), Springer: Springer Tokyo, (in Japanese) |
| [2] | Dunkl, C., A Krawtchouk polynomial addition theorem and wreath products of symmetric groups, Indiana Univ. Math. J., 25, 4, 335-358 (1976) · Zbl 0326.33008 |
| [3] | Macdonald, I. G., Symmetric Functions and Hall Polynomials (1995), Clarendon Press: Clarendon Press Oxford · Zbl 0487.20007 |
| [4] | H. Mizukawa, Zonal spherical functions of \((GrnS_nnm\); H. Mizukawa, Zonal spherical functions of \((GrnS_nnm\) · Zbl 1054.33011 |
| [5] | Yoshida, M., Hypergeometric Functions, My Love. Modular Interpretations of Configuration Spaces, Aspects of Mathematics (1997), Friedr. Vieweg and Sohn: Friedr. Vieweg and Sohn Braunschweig · Zbl 0889.33008 |
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