Gram determinants and semisimplity criteria for Birman-Wenzl algebras
Quantum Algebra
2008-02-18 v2 Representation Theory
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.
Cite
@article{arxiv.math/0607266,
title = {Gram determinants and semisimplity criteria for Birman-Wenzl algebras},
author = {Hebing Rui and Mei Si},
journal= {arXiv preprint arXiv:math/0607266},
year = {2008}
}
Comments
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