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 \({}_{n+1}\phi _n\).
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 20K03645. The author declares no conflicts of interest associated with this manuscript.
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Idomoto, T., Suzuki, T. An affine Weyl group action on the basic hypergeometric series arising from the q-Garnier system. Lett Math Phys 112, 121 (2022). https://doi.org/10.1007/s11005-022-01613-3
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DOI: https://doi.org/10.1007/s11005-022-01613-3