Spectral curves of the hyperelliptic Hitchin systems

TL;DR

This paper characterizes spectral curves and derives explicit algebraic-geometric formulas for action-angle coordinates in hyperelliptic Hitchin systems across various Lie algebra types.

Contribution

It provides a comprehensive description of spectral curves and explicit formulas for action-angle coordinates for hyperelliptic Hitchin systems, extending previous work to multiple Lie algebra types.

Findings

Explicit formulas for spectral curves and action-angle coordinates.

Applicable to all complex simple Lie algebras of types A, B, C.

Enhances understanding of integrable systems on hyperelliptic curves.

Abstract

A description of the class of spectral curves, and explicit formulas for algebraic-geometric action-angle coordinates are obtained for the Hitchin systems on hyperelliptic curves, for any complex simple Lie algebra of the types $A_l$, $B_l$, $C_l$.