Restriction theorems for homogeneous bundles

We prove that for an irreducible representation , the associated homogeneous -vector bundle Wτ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in , where k is an algebraically closed field of characteristic ≠2,3 respectively. In particular Wτ is semistable when restricted to general hypersurfaces of degree⩾2 and is strongly semistable when restricted to the generic hypersurface of degree⩾2.