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.
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