Separation of variables for type $D_n$ Hitchin systems on hyperelliptic curves

TL;DR

This paper applies separation of variables to derive explicit Darboux coordinates for Hitchin systems on hyperelliptic curves associated with type Dn Lie algebras, advancing the understanding of integrable systems in algebraic geometry.

Contribution

It provides explicit formulas for Darboux coordinates in Hitchin systems on hyperelliptic curves for type Dn Lie algebras, a novel application of separation of variables.

Findings

Explicit formulas for Darboux coordinates derived

Enhanced understanding of Hitchin systems on hyperelliptic curves

Method applicable to type Dn Lie algebras

Abstract

We use separation of variables to find explicit formulas for the Darboux coordinates for the Hitchin systems on a hyprelliptic curve for simple Lie algebras of type $D_n$.