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.

13 pages

References in corpus (3)

• A $q$-anaolg of the sixth Painlevé equation
• q-Difference equations of KdV type and "Chazy-type" second-degree difference equations
• A q-analogue of gl_3 hierarchy and q-Painleve VI

Cited by in corpus (7)

• Variations of $q$-Garnier system
• Geometric Reductions of ABS equations on an $n$-cube to discrete Painlevé systems
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)
• A $q$-analogue of the matrix sixth Painlevé system
• Tau functions of the UC hierarchy as partition functions of matrix models