The representation theory of cyclotomic BMW algebras

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dc.creatorRui, H.
dc.creatorSi, M.
dc.date2008-07-25
dc.date.accessioned2026-07-07T09:52:58Z
dc.date.available2026-07-07T09:52:58Z
dc.descriptionIn 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}.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0807.4149
dc.identifierhttp://arxiv.org/abs/0807.4149
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165788
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleThe representation theory of cyclotomic BMW algebras
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