Let G be either Sp(V) or O(V). Using an action of the Brauer algebra, we describe the subspace T-k(V-xm) subset of or equal to V-xm of tensors of valence k as an induced representation of the symmetric group S-m. As an application, we recover a special case of Littlewood's restriction rule, affording the decomposition of an irreducible GL(V)-module when restricted to G. Moreover we get an explicit realization of the irreducible representations of the Brauer algebra. (C) 1997 Academic Press.
Representations of the Brauer algebra and Littlewood's restriction rules / Fabio, Gavarini; Papi, Paolo. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 194:1(1997), pp. 275-298. [10.1006/jabr.1996.7003]
Representations of the Brauer algebra and Littlewood's restriction rules
PAPI, Paolo
1997
Abstract
Let G be either Sp(V) or O(V). Using an action of the Brauer algebra, we describe the subspace T-k(V-xm) subset of or equal to V-xm of tensors of valence k as an induced representation of the symmetric group S-m. As an application, we recover a special case of Littlewood's restriction rule, affording the decomposition of an irreducible GL(V)-module when restricted to G. Moreover we get an explicit realization of the irreducible representations of the Brauer algebra. (C) 1997 Academic Press.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.