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

S Lyle, A Mathas

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10 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)151-179
Number of pages29
JournalJournal of Algebraic Combinatorics
Volume22
Issue number2
DOIs
Publication statusPublished - 2005

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