The representation theory of cyclotomic BMW algebras

Details The representation theory of cyclotomic BMW algebras The representation theory of cyclotomic BMW algebras

2008-07-25

arxiv.org/abs/0807.4149v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

In this paper, we go on Rui-Xu's work on cyclotomic Birman-Wenzl algebras $\W_{r, n}$ in \cite{RX}. In particular, we use the representation theory of cellular algebras in \cite{GL} to classify the irreducible $\W_{r, n}$-modules for all positive integers $r$ and $n$. By constructing cell filtrations for all cell modules of $\W_{r, n}$, we compute the discriminants associated to all cell modules for $\W_{r, n} $. Via such discriminats together with induction and restriction functors given in section~5, we determine explicitly when $\W_{r, n}$ is semisimple over a field. This generalizes our previous result on Birman-Wenzl algebras in \cite{RS1}.

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