  We prove that for an irreducible representation $\tau:GL(n)\to GL(W)$, the
associated homogeneous ${\bf P}_k^n$-vector bundle $W_{\tau}$ is strongly
semistable when restricted to any smooth quadric or to any smooth cubic in
${\bf P}_k^n$, where $k$ is an algebraically closed field of characteristic
$\neq 2,3$ respectively. In particular $W_{\tau}$ is semistable when restricted
to general hypersurfaces of degree $\geq 2$ and is strongly semistable when
restricted to the $k$-generic hypersurface of degree $\geq 2$.
