Restriction theorems for homogeneous bundles

Abstract

We prove that for an irreducible representation τ: GL(n) → GL(W), the associated homogeneous Pⁿ_k-vector bundle W_τ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in Pⁿ_k, where k is an algebraically closed field of characteristic ≠2,3 respectively. In particular W_τ is semistable when restricted to general hypersurfaces of degree ≥2 and is strongly semistable when restricted to the generic hypersurface of degree ≥2.