Ordinary differential system in dinension six with affine Weyl group symmetry of type $D_4^{(2)}$

TL;DR

This paper introduces a new six-dimensional differential system with affine Weyl group symmetry of type D4^{(2)}, expanding the class of higher order Painlevé systems with novel symmetry and holomorphy properties.

Contribution

It presents the second known example of higher order Painlevé type systems of this symmetry, detailing its symmetry, holomorphy conditions, and invariant divisors.

Findings

New six-dimensional differential system with D4^{(2)} symmetry

Identification of symmetry and holomorphy conditions

Introduction of invariant divisors for the system

Abstract

We find a three-parameter family of ordinary differential systems in dimension six with affine Weyl group symmetry of type $D_4^{(2)}$. This is the second example which gave higher order Painlev\'e type systems of type $D_{4}^{(2)}$. We show that we give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new.