This book is the first set of proceedings to be devoted entirely to the theory of hypergeometric functions defined on domains of positivity. Most of the scientific areas in which these functions are applied include analytic number theory, combinatorics, harmonic analysis, random walks, representation theory, and mathematical physics--are represented here. This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida in March 1991, which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses for it contains many open problems.

Readership

Mathematicians, mathematical physicists, mathematical statisticians and graduate students seeking an introduction to the literature.

Table of Contents

• J. Angel, N. Celniker, S. Poulos, A. Terras, C. Trimble, and E. Velasquez -- Special functions on finite upper half planes
• R. J. Beerends -- Some special values for the \(BC\) type hypergeometric function
• N. Bergeron and A. M. Garsia -- On certain spaces of harmonic polynomials
• L. C. Biedenharn and J. D. Louck -- Identities for generalized hypergeometric coefficients
• P. Diaconis and P. Hanlon -- Eigen analysis for some examples of the Metropolis algorithm
• H. Ding -- Hilbert spaces of vector-valued holomorphic functions and irreducibility of multiplier representations
• C. F. Dunkl -- Hankel transforms associated to finite reflection groups
• J. Faraut -- Prolongement analytique des series de Taylor spheriques
• P. J. Hanlon, R. P. Stanley, and J. R. Stembridge -- Some combinatorial aspects of the spectra of normally distributed random matrices
• K. D. Johnson -- Degenerate principle series on tube type domains
• T. H. Koornwinder -- Askey-Wilson polynomials for root systems of type \(BC\)
• R. A. Kunze -- Some special functions in the Fock space
• M. Lassalle -- Matrice de Hua et polynômes de Jack
• Z. Yan -- Generalized hypergeometric functions and Laguerre polynomials in two variables