q-Painlev\'e systems arising from q-KP hierarchy

TL;DR

This paper derives a new class of q-Painlevé systems from the q-KP hierarchy, revealing their symmetry properties and constructing rational solutions using q-Schur functions.

Contribution

It introduces a novel connection between q-Painlevé equations and the q-KP hierarchy, including symmetry analysis and explicit rational solutions.

Findings

Derived q-Painlevé systems from q-KP hierarchy with multi-time variables.

Identified affine Weyl group symmetry of the systems.

Constructed rational solutions using q-Schur functions.

Abstract

A system of q-Painlev\'e type equations with multi-time variables t_1,...,t_M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type A^{(1)}_{M-1} \times A^{(1)}_{N-1}. Its rational solutions are constructed in terms of q-Schur functions.