Generalized q-Painlevé VI systems of type (A_2n+1+A₁+A₁)⁽¹⁾ arising from cluster algebra

2018/10/08 by Okubo, Naoto, Suzuki, Takao · 2 citations
#13F60 #17B80 #34M55 #37K35 #39A13 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1810.03252

Abstract

In this article we formulate a group of birational transformations which is isomorphic to an extended affine Weyl group of type (A_2n+1+A₁+A₁)⁽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.

Cited by

• On the geometry of a 4-dimensional extension of a q-Painlevé I equation with symmetry type A₁⁽¹⁾
• Integrable deformations of cluster maps of type D_2N

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