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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
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[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
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