Parameters for which the Lawrence-Krammer representation is reducible

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dc.creatorLevaillant, Claire I.
dc.creatorWales, David B.
dc.date2009-01-24
dc.date.accessioned2026-07-07T12:34:24Z
dc.date.available2026-07-07T12:34:24Z
dc.descriptionWe show that the Lawrence-Krammer representation based on two parameters that was used by Bigelow and independently Krammer to show the linearity of the braid group is generically irreducible, but that when its parameters are specialized to some nonzero complex numbers, the representation is reducible. To do so, we construct a representation of the BMW algebra inside the Lawrence-Krammer space. As a representation of the braid group, this representation is equivalent to the Lawrence-Krammer representation, where the two parameters of the algebra are related to the parameters of the Lawrence-Krammer representation. We give all the complex values of the parameters for which the representation is reducible and describe the invariant subspaces in some cases. We show that for these values of the parameters and other values, the BMW algebra is not semisimple.
dc.description32 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0901.3856
dc.identifierhttp://arxiv.org/abs/0901.3856
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217420
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject16G30
dc.titleParameters for which the Lawrence-Krammer representation is reducible
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