Bispectrality and separation of variables in multiparticle hypergeometric systems

Evgeny Sklyanin

Tuesday 16th December, 2008 15:00-16:00 Mathematics Building, room 204


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.

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