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,δ) with parameter δ=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.
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Rowena Paget acknowledges support from EPSRC grant GR/S18151.
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Henke, A., Paget, R. Brauer Algebras with Parameter n = 2 Acting on Tensor Space. Algebr Represent Theor 11, 545–575 (2008). https://doi.org/10.1007/s10468-008-9092-7
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DOI: https://doi.org/10.1007/s10468-008-9092-7