The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n))

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dc.creatorBlumen, Sacha C.
dc.date2006-07-03
dc.date.accessioned2026-07-07T07:17:56Z
dc.date.available2026-07-07T07:17:56Z
dc.descriptionA representation of the Birman-Wenzl-Murakami algebra BW_{t}(-q^{2n},q) exists in the centraliser algebra End_{U_q(osp(1|2n))}(V^{\otimes t}), where V is the fundamental (2n+1)-dimensional irreducible U_{q}(osp(1|2n))-module. This representation is defined using permuted R-matrices acting on V^{\otimes t}. A complete set of projections onto and intertwiners between irreducible U_{q}(osp(1|2n))-summands of V^{\otimes t} exists via this representation, proving that End_{U_q(osp(1|2n))}V^{\otimes t}) is generated by the set of permuting R-matrices acting on V^{\otimes t}. We also show that a representation of the the Iwahori-Hecke algebra H_{t}(-q) of type A_{t-1} exists in the centraliser algebra End_{U_q(osp(1|2))}[(V^{+}_{1/2})^{\otimes t}], where V^{+}_{1/2} is a two-dimensional irreducible representation of U_{q}(osp(1|2)).
dc.description46 pages, 5 figures, essentially the first part of my PhD thesis together with some further work
dc.identifierhttps://arxiv.org/abs/math/0607049
dc.identifierhttp://arxiv.org/abs/math/0607049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114122
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37 (Primary) 16G99 (Secondary)
dc.titleThe Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n))
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