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