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

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

2009-01-25

arxiv.org/abs/0901.3900v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages

Scientific paper

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.

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