Stability of Schur Functors

✍ Scribed by Alexandre I Kabanov

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 179 KB
• Volume: 195
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7049

✦ Synopsis

Symplectic resp. orthogonal Schur functors are defined on a vector space V Ž . with a non-degenerate skew-symmetric resp. symmetric bilinear form. Each of Ž . Ž Ž .. these functors determines an irreducible representation of ᒐ ᒍ V resp. ᒐ ᒌ V . We prove that if dim V is sufficiently large, then the splitting into irreducible Ž . 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 Ž . stability of the branching for the symplectic orthogonal Schur functors.