Gram determinants and semisimplity criteria for Birman-Wenzl algebras
Abstract
In this paper, we compute the Gram determinants associated to each cell module of the Birman-Wenzl algebras. As a by-product, we give the necessary and sufficient condition for semisimple Birman-Wenzl algebras over an arbitrary field.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2006
- DOI:
- arXiv:
- arXiv:math/0607266
- Bibcode:
- 2006math......7266R
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory;
- 16G99;
- 20C08
- E-Print:
- 23 pages, we rewrite the paper. In particular, we delete some elementary computation. One can use the GAP program [19] to check the required formulae for small $n$ easily