An affine Weyl group action on the basic hypergeometric series arising from the q-Garnier system

Abstract

Recently, we formulated the q-Garnier system in a framework of an extended affine Weyl group of type \(A^{(1)}_{2n+1}\times A^{(1)}_1\times A^{(1)}_1\). On the other hand, the q-Garnier system admits a particular solution in terms of the basic hypergeometric series \({}_{n+1}\phi _n\). In this article, we investigate an action of the extended affine Weyl group on \({}_{n+1}\phi _n\).