Skew Weyl modules for GLn and degree reduction for Schur algebras

We prove a strong characteristic-free analogue of the classical adjoint formula (s(lambda), s(mu)f) = (s(lambda)/(mu), J) in the ring of symmetric functions. This is done by showing that the representative of a suitably chosen functor involving a tensor product is the skew Weyl module. By "strong" we mean that this representative preserves not only Hom groups, but higher Ext groups also--a fact which can be used to compute some homological invariants of Weyl modules for GL, via recursion on degree. We use the following main tools: existence of Weyl filtrations in tensor products of Weyl modules, the Akin-Buchsbaum-Weyman constructions of Weyl modules and certain vanishing properties of Ext groups. (C) 2000 Academic Press.