THE UNIVERSAL FORM OF THE BRANCHING RULE FOR THE SYMPLECTIC GROUPS

[摘要] The classical branching rule for the symplectic group describes the decomposition of the Schur module L lambda of GL(2n, C), where lambda(1) less than or equal to n, into a direct sum of irreducible representations of Sp(2n, C) under the embedding Sp(2n, C)hooked right arrow GL(2,1, C). 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. (C) 1994 Academic Press, Inc.

[发布日期] 1994-08-15