On an Integrable System of q-Difference Equations Satisfied by the Universal Characters: Its Lax Formalism and an Application to q-Painlevé Equations

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-Painlevé equations via similarity reduction. In particular a higher order analogue of the q-Painlevé VI equation is presented.