Coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of type $D_6^{(1)}$, II

TL;DR

This paper reformulates a six-parameter family of coupled Painlevé VI systems with affine Weyl group symmetry of type D6^{(1)} by analyzing their symmetry and holomorphy properties, providing new insights into their structure.

Contribution

It introduces a novel reformulation of coupled Painlevé VI systems emphasizing their symmetry and holomorphy, linked to affine Weyl group D6^{(1)}.

Findings

New symmetry-based reformulation of coupled Painlevé VI systems

Enhanced understanding of holomorphy properties in these systems

Clarification of the role of affine Weyl group D6^{(1)} in system structure

Abstract

We give a reformulation of a six-parameter family of coupled Painlev\'e VI systems with affine Weyl group symmetry of type $D_6^{(1)}$ from the viewpoint of its symmetry and holomorphy properties.