Commuting Families in Temperley-Lieb Algebras

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dc.creatorHalverson, Tom
dc.creatorMazzocco, Manuela
dc.creatorRam, Arun
dc.date2007-10-02
dc.date.accessioned2026-07-07T08:33:36Z
dc.date.available2026-07-07T08:33:36Z
dc.descriptionWe define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements in the affine Hecke algebra of type A, which in turn come from the Casimir element of the quantum group $U_h\mathfrak{gl}_n$. We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0710.0596
dc.identifierhttp://arxiv.org/abs/0710.0596
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139185
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject20G05; 16G99
dc.titleCommuting Families in Temperley-Lieb Algebras
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