On an integrable system of q-difference equations satisfied by the universal characters: its Lax formalism and an application to q-Painleve 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-Painleve equations via similarity reduction. In particular a higher-order analogue of the q-Painleve VI equation is presented.