On an integrable system of q-difference equations satisfied by the universal characters: its Lax formalism and an application to q-Painleve equations

TL;DR

This paper introduces the lattice q-UC hierarchy, an integrable system of q-difference equations related to universal characters, and demonstrates its connection to q-Painleve equations through Lax formalism and similarity reduction.

Contribution

It presents the lattice q-UC hierarchy as an extension of the q-KP hierarchy, providing its Lax formalism and linking it to higher-order q-Painleve equations.

Findings

Defined the lattice q-UC hierarchy as a compatibility condition.

Established the Lax formalism for the hierarchy.

Derived a higher-order q-Painleve VI analogue.

Abstract

The universal character is a generalization of the Schur function attached to a pair of partitions. We study an integrable system of q-difference equations satisfied by the universal characters, which is an extension of the q-KP hierarchy and is called the lattice q-UC hierarchy. We describe the lattice q-UC hierarchy as a compatibility condition of its associated linear system (Lax formalism) and explore an application to the q-Painleve equations via similarity reduction. In particular a higher-order analogue of the q-Painleve VI equation is presented.