$q$-Middle Convolution and $q$-Painlevé Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Shoko Sasaki¹  Shun Takagi¹  Kouichi Takemura² 

[1] Department of Mathematics, Faculty of Science and Engineering, Chuo University;Department of Mathematics, Ochanomizu University

关键词: $q$-Painlevé equation;    $q$-Heun equation;    middle convolution;    integral transformation.;   

DOI  :  10.3842/SIGMA.2022.056

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.

【 授权许可】

Unknown