Integral equations for Heckman-Opdam hypergeometric functions and the quantum hyperbolic Calogero-Moser system

Martin Hallnas (Chalmers and University of Gothenburg)

Tuesday 30th June 16:00-17:00
Maths 110

Abstract

Motivated by spherical functions theory, Heckman and Opdam introduced in the late 1980s hypergeometric functions associated with root systems as joint eigenfunctions of a commutative algebra of Weyl group invariant PDOs, which are related by conjugation to quantum integrals of the hyperbolic Calogero-Moser system. In this talk, I will consider the type A case and show that the corresponding hypergeometric functions satisfy a one-parameter family of explicit integral equations. I will also discuss an interpretation of the result in terms of a so-called Q-operator for the hyperbolic Calogero-Moser system and an application to bispectrality of the system.

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