Henke, A. and Paget, R. (2008) Brauer algebras with parameter n = 2 acting on tensor space. Algebras and Representation Theory, 11 (6). pp. 545-575. ISSN 1386-923X.
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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.
|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:||27 Jan 2012 14:34|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/736 (The current URI for this page, for reference purposes)|
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