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arXiv · 2201.03960

$q$-Middle Convolution and $q$-Painlev\'e Equation

Shoko Sasaki·Shun Takagi·Kouichi Takemura
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Abstract

A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlev\'e VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlev\'e VI equation. We deduce an integral transformation on the $q$-Heun equation.

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Shoko Sasaki, Shun Takagi, Kouichi Takemura. 2022-01-11. $q$-Middle Convolution and $q$-Painlev\'e Equation. https://doi.org/10.3842/sigma.2022.056

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