2022年4月25日
Generalized q-Painlevé VI Systems of Type (A2n+1+A1+A1)(1) Arising From Cluster Algebra
International Mathematics Research Notices
- ,
- 巻
- 2022
- 号
- 9
- 開始ページ
- 6561
- 終了ページ
- 6607
- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/imrn/rnaa283
- 出版者・発行元
- Oxford University Press (OUP)
Abstract
In this article we formulate a group of birational transformations that is isomorphic to an extended affine Weyl group of type $(A_{2n+1}+A_1+A_1)^{(1)}$ with the aid of mutations and permutations of vertices to a mutation-periodic quiver on a torus. This group provides a class of higher order generalizations of Jimbo–Sakai’s $q$-Painlevé VI equation as translations on a root lattice. Then the known three systems are obtained again: the $q$-Garnier system, a similarity reduction of the lattice $q$-UC hierarchy, and a similarity reduction of the $q$-Drinfeld–Sokolov hierarchy.
In this article we formulate a group of birational transformations that is isomorphic to an extended affine Weyl group of type $(A_{2n+1}+A_1+A_1)^{(1)}$ with the aid of mutations and permutations of vertices to a mutation-periodic quiver on a torus. This group provides a class of higher order generalizations of Jimbo–Sakai’s $q$-Painlevé VI equation as translations on a root lattice. Then the known three systems are obtained again: the $q$-Garnier system, a similarity reduction of the lattice $q$-UC hierarchy, and a similarity reduction of the $q$-Drinfeld–Sokolov hierarchy.
- リンク情報
- ID情報
-
- DOI : 10.1093/imrn/rnaa283
- ISSN : 1073-7928
- eISSN : 1687-0247