-Middle Convolution and -Painlevé Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Authors: Sasaki, Shoko, Takagi, Shun, Takemura, Kouichi
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211731
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: -Middle Convolution and -Painlevé Equation. Shoko Sasaki, Shun Takagi and Kouichi Takemura. SIGMA 18 (2022), 056, 21 pages

A -deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear -difference equation associated with the -Painlevé VI equation. Then we obtain integral transformations. We investigate the -middle convolution in terms of the affine Weyl group symmetry of the -P...