On an integrable system of q-difference equations satisfied by the universal characters: its Lax formalism and an application to q-Painlevé equations
نویسنده
چکیده
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.
منابع مشابه
Universal character and q-difference Painlevé equations with affine Weyl groups
The universal character is a polynomial attached to a pair of partitions and is a generalization of the Schur polynomial. In this paper, we introduce an integrable system of q-difference lattice equations satisfied by the universal character, and call it the lattice q-UC hierarchy. We regard it as generalizing both q-KP and q-UC hierarchies. Suitable similarity and periodic reductions of the hi...
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