Hitchin Pairs for non-compact real Lie groups

Abstract

Hitchin pairs on Riemann surfaces are generalizations of Higgs bundles, allowing the Higgs field to be twisted by an arbitrary line bundle. We consider this generalization in the context of $G$-Higgs bundles for a real reductive Lie group $G$. We outline the basic theory and review some selected results, including recent results by Nozad and the author arXiv:1602.02712 [math.AG] on Hitchin pairs for the unitary group of indefinite signature $\mathrm{U}(p,q)$.

Contribution to the special volume of Travaux Mathématiques dedicated to GEOQUANT 2015, comments welcome, 14 pages; v2: added references and improved introduction

References in corpus (3)

• Nonabelianization of Higgs bundles
• Spectral data for U(m,m)-Higgs bundles
• Birationality of moduli spaces of twisted $\mathrm{U}(p,q)$-Higgs bundles