On vector bundles over moduli spaces trivial on Hecke curves

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

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