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arXiv · 2207.03185

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

Taiki Idomoto·Takao Suzuki
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Abstract

Recently, we formulated the $q$-Garnier system and its variations as translations of an extended affine Weyl group of type $A^{(1)}_{2n+1}\times A^{(1)}_1\times A^{(1)}_1$. On the other hand, those systems admit particular solutions 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 ${}_{n+1}\phi_n$.

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Taiki Idomoto, Takao Suzuki. 2022-07-07. An affine Weyl group action on the basic hypergeometric series arising from the $q$-Garnier system. https://doi.org/10.1007/s11005-022-01613-3

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