Principal co-Higgs bundles on $\mathbb{P}^1$

TL;DR

This paper characterizes the semistability of principal G-co-Higgs bundles on the complex projective line using Lie theory and describes the moduli space stratification based on Harder-Narasimhan types.

Contribution

It provides a Lie-theoretic criterion for semistability and describes the moduli space stratification for principal G-co-Higgs bundles on .

Findings

Semistability characterized by simple roots of a Borel subgroup.

Stratification of the moduli space by Harder-Narasimhan types.

Explicit description for principal G-co-Higgs bundles on .

Abstract

For complex connected, reductive, affine, algebraic groups $G$, we give a Lie-theoretic characterization of the semistability of principal $G$-co-Higgs bundles on the complex projective line $\mathbb{P}^1$ in terms of the simple roots of a Borel subgroup of $G$. We describe a stratification of the moduli space in terms of the Harder-Narasimhan type of the underlying bundle.