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.
(doi:10.1007/s10468-008-9092-7)
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Official URL http://dx.doi.org/10.1007/s10468-008-9092-7 |

## 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,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 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/736 (The current URI for this page, for reference purposes) |

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