Abstract :
We prove a strong characteristic-free analogue of the classical adjoint formula sλ, sμf = sλ/μ, f 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 GLn 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.
