Abstract :
The classical branching rule for the symplectic group describes the decomposition of the Schur module Lλ of GL(2n, image), where λ1 ≤ n, into a direct sum of irreducible representations of Sp(2n, image) under the embedding Sp(2n, image) right arrow-hooked GL(2n, image). The purpose of this paper is to extend the classical branching rule to the characteristic-free case by means of explicit universal filtrations. As an application of our methods, we describe universal resolutions of the fundamental representations of the symplectic groups in terms of the fundamental representations of the corresponding general linear groups.
