zbMATH — the first resource for mathematics

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.

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
05E05 Symmetric functions and generalizations
Full Text: DOI
[1] Aomoto, K.; Kita, M., Theory of hypergeometric functions, (1994), 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 Oxford · Zbl 0487.20007
[4] H. Mizukawa, Zonal spherical functions of (G(r,1,n),Sn) and (n+1,m+1)-hypergeometric functions, Adv. Math., in press. · Zbl 1054.33011
[5] Yoshida, M., Hypergeometric functions, my love. modular interpretations of configuration spaces, aspects of mathematics, (1997), Friedr. Vieweg and Sohn Braunschweig · Zbl 0889.33008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.