  Let $M_X(r,\xi)$ be the moduli space of stable vector bundles, on a smooth
complex projective curve $X$, of rank $r$ and fixed determinant $\xi$ such that
$\deg(\xi)$ is coprime to $r$. If $E$ is a vector bundle $M_X(r,\xi)$ whose
restriction to every Hecke curve in $M_X(r,\xi)$ is trivial, we prove that $E$
is trivial.
