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 2 deg ( Λ ) , also dualization of vector bundles.