Hitchin systems for invariant and anti-invariant vector bundles

Abstract

Given a smooth projective complex curve X X with an involution σ \sigma , we study the Hitchin systems for the locus of anti-invariant (resp. invariant) stable vector bundles over X X under σ \sigma . Using these integrable systems and the theory of the nilpotent cone, we study the irreducibility of these loci. The anti-invariant locus can be thought of as a generalisation of Prym varieties to higher rank.