Zonal spherical functions on the complex reflection groups and (n+1,m+1)-hypergeometric functions |
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Authors: | Hiroshi Mizukawa |
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Institution: | Division of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
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Abstract: | The pair of groups, complex reflection group G(r,1,n) and symmetric group Sn, is a Gelfand pair. Its zonal spherical functions are expressed in terms of multivariate hypergeometric functions called (n+1,m+1)-hypergeometric functions. Since the zonal spherical functions have orthogonality, they form discrete orthogonal polynomials. Also shown is a relation between monomial symmetric functions and the (n+1,m+1)-hypergeometric functions. |
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Keywords: | 33C45 05E35 05E05 |
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