Hook interpolations

The hook components of V n interpolate between the symmetric power Symn(V) and the exterior power n(V). When V is the vector space of k×m matrices over C, we decompose the hook components into irreducible GLk(C)×GLm(C)-modules. In particular, classical theorems are proved as boundary cases. For the algebra of square matrices over C, a bivariate interpolation is presented and studied.