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Representations of the Brauer Algebra and Littlewood's Restriction Rules

✍ Scribed by Fabio Gavarini; Paolo Papi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 304 KB
Volume: 194
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.7003

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✦ Synopsis

Let G be either Sp V or O V . Using an action of the Brauer algebra, we k Ž mm . mm describe the subspace T V :V of tensors of valence k as an induced representation of the symmetric group S . As an application, we recover a special m case of Littlewood's restriction rule, affording the decomposition of an irreducible Ž . GL V -module when restricted to G. Moreover we get an explicit realization of the irreducible representations of the Brauer algebra.

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