Brauer algebras with parameter n = 2 acting on tensor space

Henke, Anne and Paget, Rowena E. (2008) Brauer algebras with parameter n = 2 acting on tensor space. Algebras and Representation Theory, 11 (6). pp. 545-575. ISSN 1386-923X. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Let k be a field of prime characteristic p and E an n-dimensional vector space. We completely describe the tensor space E-r viewed as a module for the Brauer algebra B (k) (r,delta) with parameter delta=2 and n=2. This description shows that while the tensor space still affords Schur-Weyl duality, it typically is not filtered by cell modules, and thus will not be equal to a direct sum of Young modules as defined in Hartmann and Paget (Math Z 254:333-357, 2006). This is very different from the situation for group algebras of symmetric groups. Other results about the representation theory of these Brauer algebras are obtained, including a new description of a certain class of irreducible modules in the case when the characteristic is two.

Item Type: Article
Uncontrolled keywords: Brauer algebras; Tensor space; Schur-Weyl duality; 20G05
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:27
Last Modified: 03 Jun 2014 10:14
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