An elliptic hypergeometric integral with W(F_4) symmetry

TL;DR

This paper introduces a new transformation for elliptic hypergeometric integrals exhibiting F_4 Weyl group symmetry, generalizing previous series transformations and exploring limits to basic hypergeometric functions.

Contribution

It presents a novel transformation between elliptic hypergeometric beta integrals that reveals F_4 Weyl group symmetry, extending prior series transformations.

Findings

New elliptic hypergeometric integral transformation with F_4 symmetry

Generalization of existing series transformation by Langer, Schlosser, and Warnaar

Limits to basic hypergeometric functions as p approaches 0

Abstract

In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F_4. The transformation is a generalization of a series transformation discovered by Langer, Schlosser, and Warnaar. Moreover we consider various limits of this transformation to basic hypergeometric functions obtained by letting p tend to 0.