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SIGMA, 2017, Volume 13, 092, 18 pages (Mi sigma1292)  

This article is cited in 2 scientific papers (total in 2 papers)

A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$

Hidehito Nagao

Department of Arts and Science, National Institute of Technology, Akashi College, Hyogo 674-8501, Japan

Abstract: Recently a certain $q$-Painlevé type system has been obtained from a reduction of the $q$-Garnier system. In this paper it is shown that the $q$-Painlevé type system is associated with another realization of the affine Weyl group symmetry of type $E_7^{(1)}$ and is different from the well-known $q$-Painlevé system of type $E_7^{(1)}$ from the point of view of evolution directions. We also study a connection between the $q$-Painlevé type system and the $q$-Painlevé system of type $E_7^{(1)}$. Furthermore determinant formulas of particular solutions for the $q$-Painlevé type system are constructed in terms of the terminating $q$-hypergeometric function.

Keywords: $q$-Painlevé system of type $E_7^{(1)}$; $q$-Garnier system; Padé method; $q$-hypergeometric function.

Funding Agency
This work was partially supported by Expenses Revitalizing Education and Research of Akashi College (0217030).


DOI: https://doi.org/10.3842/SIGMA.2017.092

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Bibliographic databases:

MSC: 14H70; 33D15; 33D70; 34M55; 37K20; 39A13; 41A21
Received: July 3, 2017; in final form November 24, 2017; Published online December 10, 2017
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Citation: Hidehito Nagao, “A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$”, SIGMA, 13 (2017), 092, 18 pp.

Citation in format AMSBIB
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\by Hidehito~Nagao
\paper A Variation of the $q$-Painlev\'e System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
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\vol 13
\papernumber 092
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\crossref{https://doi.org/10.3842/SIGMA.2017.092}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. H. Nagao, Ya. Yamada, “Study of q-Garnier system by Padé method”, Funkc. Ekvacioj-Ser. Int., 61:1 (2018), 109–133  crossref  mathscinet  isi
    2. H. Nagao, Ya. Yamada, “Variations of the q-Garnier system”, J. Phys. A-Math. Theor., 51:13 (2018), 135204  crossref  mathscinet  zmath  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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