2008/11/19 by Teruhisa Tsuda, Tsuda, Teruhisa
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0811.3112
openalex publication_date 2008/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 hierarchy yield the q-difference Painleve equations of types A2g+1(1) (g ≥ 1), D5(1), and E6(1). As its consequence, a class of algebraic solutions of the q-Painleve equations is rapidly obtained by means of the universal character. In particular, we demonstrate explicitly the reduction procedure for the case of type E6(1), via the framework of tau-functions based on the geometry of certain rational surfaces.