Work

Reducibility of symmetry on $q$-Painlevé equations

Year: 2026

Type: preprint

Abstract: It is known that $q$-Painlevé equations admit the symmetry of the extended affine Weyl groups. Kajiwara, Noumi and Yamada developed a unified description of the symmetry by introducing representations of the extended affine Weyl groups. On the other hand, a parallel translation associated with the extended affine Weyl groups describes the time evolution in Sakai's theory of discrete Painlevé equations. In this paper, we introduce the equivalences to the representations of Kajiwara, Noumi and Yamada. The equivalences imply reducibility of the representations, and they are related to the expressions of the parallel translations of the $q$-Painlevé equations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02927

Authors: Sato, Chihiro, Takemura, Kouichi, Yamashita, Ohka

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Difference equations and differential equations associated with accessory parameters

OpenAlex ID: W7208779143

Cites: 2

Cited by:

Related to: 10