Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces

TL;DR

This paper introduces a classification of homogeneous principal Higgs and co-Higgs bundles on irreducible Hermitian symmetric spaces of compact type, establishing their moduli spaces and advancing understanding in geometric structures on symmetric spaces.

Contribution

It provides the first classification of homogeneous Higgs and co-Higgs bundles on these symmetric spaces, including their moduli spaces and isomorphism classes.

Findings

Classification of homogeneous Higgs bundles

Classification of homogeneous co-Higgs bundles

Description of their moduli spaces

Abstract

We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to isomorphism, which in each case can be interpreted as defining a moduli space.