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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 056, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.056 (Mi sigma1852) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

Shoko Sasakia, Shun Takagia, Kouichi Takemurab

a Department of Mathematics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
b Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
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DOI: https://doi.org/10.3842/SIGMA.2022.056
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 $q$-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.
Keywords: $q$-Painlevé equation, $q$-Heun equation, middle convolution, integral transformation.
Funding agency Grant number
Japan Society for the Promotion of Science JP18K03378
The third author was supported by JSPS KAKENHI Grant Number JP18K03378.
Received: January 31, 2022; in final form July 8, 2022; Published online July 20, 2022
Bibliographic databases:
Document Type: Article
MSC: 33E10, 34M55, 39A13
Language: English
Citation: Shoko Sasaki, Shun Takagi, Kouichi Takemura, “$q$-Middle Convolution and $q$-Painlevé Equation”, SIGMA, 18 (2022), 056, 21 pp.
Citation in format AMSBIB
\Bibitem{SasTakTak22}
\by Shoko~Sasaki, Shun~Takagi, Kouichi~Takemura
\paper $q$-Middle Convolution and $q$-Painlev\'e Equation
\jour SIGMA
\yr 2022
\vol 18
\papernumber 056
\totalpages 21
\mathnet{http://mi.mathnet.ru/sigma1852}
\crossref{https://doi.org/10.3842/SIGMA.2022.056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4454174}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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