Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules

Lyle, S and Mathas, A (2005) Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules. Journal of Algebraic Combinatorics, 22 (2). pp. 151-179. ISSN 0925-9899

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Abstract

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,d) with parameter d=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
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:52
Last Modified: 24 Jul 2019 16:24
URI: https://ueaeprints.uea.ac.uk/id/eprint/20728
DOI: 10.1007/s10801-005-2511-5

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