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

Taiki Idomoto, Takao Suzuki

Recently, we formulated the $q$-Garnier system and its variations as translations of an extended affine Weyl group of type $A_{2n+1}^{(1)}\times A_1^{(1)}\times A_1^{(1)}$. On the…