Abstract
The pair of groups, complex reflection group G( r,1, n) and symmetric group S n , 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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