PreprintCC BY 4.0arXiv
Reducibility of symmetry on q-Painlevé equations
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.
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BibTeX
@misc{sato2026reducibility,
title = {{Reducibility of symmetry on $q$-Painlevé equations}},
author = {Chihiro Sato and Kouichi Takemura and Ohka Yamashita},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02927},
eprint = {2609.02927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02927},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reducibility of symmetry on q-Painlevé equations
AU - Chihiro Sato
AU - Kouichi Takemura
AU - Ohka Yamashita
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.02927
UR - https://arxiv.org/abs/2609.02927
AB - 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.
ER -