EVENT DETAILS AND ABSTRACT

Title: Transformations of elliptic hypergeometric integrals
Speaker: Eric Rains
Speaker Info: CalTech
Brief Description:
Special Note:
Abstract:

Euler's beta (and gamma) integral lies at the core of much of the theory of special functions, and many generalizations have been studied, including multivariate analogues (the Selberg integral; also work of Dixon and Varchenko), q-analogues (Askey-Wilson, Nasrallah-Rahman), and both (work of Milne-Lilly and Gustafson). Recently, van Diejen and Spiridonov have conjectured several generalizations going beyond q to the elliptic level (replacing q by a point on an elliptic curve). I'll discuss how a simple question in random matrix theory led to a proof of their conjectured identities, in fact generalizing them to a transformation (à la the integral representation of hypergeometric functions). I'll also discuss an elliptic Selberg integral with a (partial) symmetry under the Weyl group E₈, as well as connections with the theory of Koornwinder polynomials.