A reformulation of the generalized q-Painlevé VI system with W(A⁽¹⁾_2n+1) symmetry

2016/02/04 by Suzuki, Takao · 1 citation
#33D15 #34M55 #39A13 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1602.01573

Abstract

In the previous work we introduced the higher order q-Painlevé system q-P_(n+1,n+1) as a generalization of the Jimbo-Sakai's q-Painlevé VI equation. It is derived from a q-analogue of the Drinfeld-Sokolov hierarchy of type A⁽¹⁾_2n+1 and admits a particular solution in terms of the Heine's q-hypergeometric function _n+1ϕ_n. However the obtained system is insufficient as a generalization of q-P_\rmVI due to some reasons. In this article we rewrite the system q-P_(n+1,n+1) to a more suitable one.

Cited by

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

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