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.

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

Cited by in corpus (3)

• The Cyclotomic Birman-Murakami-Wenzl Algebras
• Irreducibility of the Lawrence-Krammer representation of the BMW algebra of type $A_{n-1}$, PhD thesis California Institute of Technology 2008
• Parameters for which the Lawrence-Krammer representation is reducible