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Chihiro Sato

Publications and source records attributed to Chihiro Sato.

2 recordsLinked to original sources
arXiv2026

Reducibility of symmetry on $q$-Painlev\'e equations

It is known that $q$-Painlev\'e 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 Painlev\'e 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 $q$-Painlev\'e equations.

math.CA↗
arXiv2025

Degenerations of $q$-Heun equation

We obtain several degenerations of the $q$-Heun equation by considering the linear $q$-difference equations associated to several $q$-Painlev\'e equations. We establish definitions of the confluent $q$-Heun equation, the biconfluent $q$-Heun equation and the doubly confluent $q$-Heun equation, and investigate limit procedures to the corresponding differential equations.

math.CA↗