Automorphisms of moduli spaces of vector bundles over a curve

Abstract

Let X be an irreducible smooth complex projective curve of genus g≥4. Let M(r,Λ) be the moduli space of stable vector bundles E⟶X or rank r and fixed determinant Λ. We show that the automorphism group of M(r,Λ) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, in case r divides 2deg(Λ), also dualization of vector bundles.