Stability of Schur functors

[摘要] Symplectic (resp. orthogonal) Schur functors are defined on a vector space V with a non-degenerate skew-symmetric (resp. symmetric) bilinear form. Each of these functors determines an irreducible representation of sp(V) (resp. so(V)). We prove that if dim V is sufficiently large, then the splitting into irreducible components of the composition of a symplectic (orthogonal) Schur functor and an ordinary Schur functor applied to V is independent of dim V. We also prove the stability of the branching for the symplectic (orthogonal) Schur functors. (C) 1997 Academic Press.

[发布日期] 1997-09-01