### Bispectrality and separation of variables in multiparticle hypergeometric systems

Sklyanin, E *(York)*

Thursday 26 March 2009, 11:30-12:30

Meeting Room 3, CMS

#### Abstract

Hypergeometric functions depending on two sets of parameters are known to possess the property of bispectrality: they satisfy simultaneously to two different systems of differential/difference equation in one set of parameter, the other set playing the role of spectral parameters and vice versa. The examples we discuss include the open Toda lattice, Calogero-Sutherland system, KZ-equation. We shall also review the recent results on the relation of bispectrality to the separation of variables, Baxter's Q-operator and Givental integral representations.