Universal character and q-difference Painlevé equations with affine Weyl groups
| dc.creator | Tsuda, Teruhisa | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:19:29Z | |
| dc.date.available | 2026-07-07T10:19:29Z | |
| dc.description | 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 $A_{2g+1}^{(1)}$ $(g \geq 1)$, $D_5^{(1)}$, and $E_6^{(1)}$. 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 $E_6^{(1)}$, via the framework of tau-functions based on the geometry of certain rational surfaces. | |
| dc.description | This is a revised version of the manuscript: UTMS2005-21 (Preprint, 2005) | |
| dc.identifier | https://arxiv.org/abs/0811.3112 | |
| dc.identifier | http://arxiv.org/abs/0811.3112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174527 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Universal character and q-difference Painlevé equations with affine Weyl groups | |
| dc.type | text |