Skew Weyl modules for \(\text{GL}_n\) and degree reduction for Schur algebras (Q1975149)

The author proves a characteristic-free analogue of the classical adjoint formula \(\langle s_\lambda,s_\mu f\rangle=\langle s_{\lambda/\mu},f\rangle\) in the ring of symmetric functions. This is done by showing that the representative of a suitably chosen functor involving a tensor product is a skew Weyl module. It is shown (Theorem 2) that this representative preserves Hom groups and higher Ext groups.