Quivers and difference Painleve equations

TL;DR

This paper constructs Lax pairs for difference Painleve equations associated with affine Weyl groups E6, E7, and E8, demonstrating their role as symmetries of specific Fuchsian systems.

Contribution

It introduces natural Lax pairs for these equations, linking them to Fuchsian systems and affine Weyl symmetries, advancing understanding of their integrable structure.

Findings

Lax pairs for difference Painleve equations with E6, E7, E8 symmetry groups

Connection between these equations and Fuchsian systems

Identification of affine Weyl group symmetries in the equations

Abstract

We will describe natural `Lax pairs' for the difference Painleve equations with affine Weyl symmetry groups of types E6, E7 and E8, showing that they do indeed arise as symmetries of certain Fuchsian systems of differential equations.