On a matrix element representation of the GKZ hypergeometric functions

This talk is based on my joint paper with A.A. Gerasimov and S.V. Oblezin (arXiv: 2209.02516 v1[math.RT] 6 Sep 2022).
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 $gl_{\ell+1} (R)$, another matrix element representation in terms of $L_{\ell(\ell+1)}$.