Recurrences for elliptic hypergeometric integrals
Abstract
In recent work (math.QA/0309252) on multivariate hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E_7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of two flavors: linear recurrences that hold only up to dimension 6, and three families of bilinear recurrences that hold in arbitrary dimension, subject to a condition on the parameters. As a corollary, we find that a codimension one special case of the integral is a tau function for the elliptic Painlev\'e equation.
Cite
@article{arxiv.math/0504285,
title = {Recurrences for elliptic hypergeometric integrals},
author = {Eric M. Rains},
journal= {arXiv preprint arXiv:math/0504285},
year = {2007}
}
Comments
16 pages LaTeX. From workshop on Elliptic Integrable Systems, RIMS 11/2004