On symmetry of q-Painlev\'e equations and associated linear equations

TL;DR

This paper explores the symmetry properties of linear q-difference equations linked to q-Painlevé equations, enhancing understanding of their time evolution through Weyl group symmetry.

Contribution

It reveals the symmetry structure of associated linear equations and refines the expression of time evolution in q-Painlevé equations using Weyl group symmetry.

Findings

Identified symmetry of linear q-difference equations

Adjusted time evolution expressions for q-Painlevé equations

Connected symmetry properties with Weyl group actions

Abstract

We investigate the symmetry of the linear q-difference equations which are associated with some q-Painlev\'e equations. We apply it for adjustment of the expression of the time evolution on the q-Painlev\'e equations in terms of the Weyl group symmetry.