On matrix element representation of the GKZ hypergeometric functions

Abstract

In the talk, l shall present our joint paper with A.Gerasimov and D.Lebedev. in this paper, wedevelop a representation theory approach to the study of generalized hypergeometric functions ofGelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may beidentified with matrix elements of non-reductive Lie algebras L(N) of oscillator type. The Whittakerfunctions associated with principal series representations of gl(n, R) being special cases of GKZhypergeometric functions, thus admit along with a standard matrix element representationsassociated with reductive Lie algebra gl(n, R), another matrix element representation in terms ofL(n(n-1)).