A new generalization of Hermite’s reciprocity law

Abstract

Given a partition λ of n, the Schur functor (Formula presented.) associates to any complex vector space V, a subspace (Formula presented.) of (Formula presented.). Hermite’s reciprocity law, in terms of the Schur functor, states that (Formula presented.). (Formula presented.). We extend this identity to many other identities of the type (Formula presented.).