On matrix element representation of the GKZ hypergeometric functions

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

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

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