On a matrix element representation of the GKZ hypergeometric functions

Abstract

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 ${\mathfrak{L}}_N$ of oscillator type. The Whittaker functions associated with principal series representations of ${\mathfrak{gl}}_{\ell +1}(\mathbb{R})$ being special cases of GKZ hypergeometric functions, thus admit along with a standard matrix element representations associated with reductive Lie algebra ${\mathfrak{gl}}_{\ell +1}(\mathbb{R})$, another matrix element representation in terms of ${\mathfrak{L}}_{\ell (\ell +1)}$.

24 pages

References in corpus (2)

• Baxter operator and Archimedean Hecke algebra
• On a matrix element representation of the GKZ hypergeometric functions

Cited by in corpus (1)

• On a matrix element representation of the GKZ hypergeometric functions