Holomorphy conditions of Fuji-Suzuki coupled Painlev\'e VI system

TL;DR

This paper investigates the holomorphy conditions of the Fuji-Suzuki coupled Painlevé VI system, introduces translation operators, and explores a confluence process to the Noumi-Yamada system, enhancing understanding of their interrelations.

Contribution

It provides new holomorphy conditions, defines translation operators on parameters, and describes a confluence process connecting Fuji-Suzuki and Noumi-Yamada systems.

Findings

Holomorphy conditions for Fuji-Suzuki system established.

Two translation operators acting on parameter η introduced.

Confluence process from Fuji-Suzuki to Noumi-Yamada system described.

Abstract

In this note, we give some holomorphy conditions of Fuji-Suzuki coupled Painlev\'e VI system. We also give two translation operators acting on the constant parameter $\eta$. We note a confluence process from the Fuji-Suzuki system to the Noumi-Yamada system of type $A_5^{(1)}$.