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Generalized $q$-Painlev\'e VI systems of type $(A_{2n+1}+A_1+A_1)^{(1)}$ arising from cluster algebra. (arXiv:1810.03252v1 [math.QA])
来源于:arXiv
In this article we formulate a group of birational transformations which 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 to a mutation-periodic quiver on a
torus. This group provides four types of generalizations of Jimbo-Sakai's
$q$-Painlev\'e VI equation as translations of the affine Weyl group. 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. 查看全文>>
