Spectral data for G-Higgs bundles

TL;DR

This paper introduces a geometric approach to understanding principal G-Higgs bundles via spectral data, focusing on split real forms and specific groups like SL(2,R), U(p,p), SU(p,p), and Sp(2p,2p).

Contribution

It develops a novel geometric method for analyzing principal G-Higgs bundles through spectral data, especially for real forms of complex Lie groups.

Findings

Spectral data characterizes principal G-Higgs bundles for various real forms.

Applications demonstrate the utility of the spectral data approach.

Open questions suggest directions for future research.

Abstract

We develop a new geometric method of understanding principal G-Higgs bundles through their spectral data, for G a real form of a complex Lie group. In particular, we consider the case of G a split real form, as well as G = SL(2,R), U(p,p), SU(p,p), and Sp(2p,2p). Further, we give some applications of our results, and discuss open questions.