Irreducibility of the Lawrence-Krammer representation of the BMW algebra of type $A_{n-1}$

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dc.creatorLevaillant, Claire Isabelle
dc.date2008-10-17
dc.date2008-10-30
dc.date.accessioned2026-07-07T10:13:48Z
dc.date.available2026-07-07T10:13:48Z
dc.descriptionIt is known that the Lawrence-Krammer representation of the Artin group of type $A_{n-1}$ based on the two parameters $t$ and $q$ that was used by Krammer and independently by Bigelow to show the linearity of the braid group on $n$ strands is generically irreducible. Here, we recover this result and show further that for some complex specializations of the parameters the representation is reducible. We give all the values of the parameters for which the representation is reducible as well as the dimensions of the invariant subspaces. We deduce some results of semisimplicity of the Birman-Murakami-Wenzl algebra of type $A_{n-1}$.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0810.3205
dc.identifierhttp://arxiv.org/abs/0810.3205
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172658
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject16G32
dc.titleIrreducibility of the Lawrence-Krammer representation of the BMW algebra of type $A_{n-1}$
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