Automorphisms of moduli spaces of vector bundles over a curve

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,Λ) be the moduli space of stable vector bundles over X or rank r and fixed determinant Λ, of degree d. We give a new proof of the fact that the automorphism group of M(r,Λ) is generated by automorphisms of the curve X, tensorization with suitable line bundles, and, if r divides 2d, also dualization of vector bundles.

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