Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations

TL;DR

This paper explores how degenerations of Ruijsenaars-van Diejen operators relate to q-Painleve equations, establishing difference analogues of the Painleve-Heun correspondence in integrable systems.

Contribution

It introduces a novel connection between degenerations of Ruijsenaars-van Diejen operators and q-Painleve equations, extending the Painleve-Heun correspondence to difference equations.

Findings

Degenerations lead to new q-Painleve equations

Difference analogues of Painleve-Heun correspondence established

Provides a framework for understanding integrable difference systems

Abstract

It is known that the Painleve VI is obtained by connection preserving deformation of some linear differential equations, and the Heun equation is obtained by a specialization of the linear differential equations. We inverstigate degenerations of the Ruijsenaars-van Diejen difference opearators and show difference analogues of the Painleve-Heun correspondence.