Zonal spherical functions on the complex reflection groups and (n+1, m+1)-hypergeometric functions

摘要

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. (C) 2003 Elsevier Science (USA). All rights reserved.