Automorphisms of moduli spaces of vector bundles over a curve

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