COMMUTING FAMILIES IN HECKE AND TEMPERLEY-LIEB ALGEBRAS
AuthorHalverson, T; Mazzocco, M; Ram, A
Source TitleNagoya Mathematical Journal
University of Melbourne Author/sRam, Arun
AffiliationMathematics and Statistics
Document TypeJournal Article
CitationsHalverson, T., Mazzocco, M. & Ram, A. (2009). COMMUTING FAMILIES IN HECKE AND TEMPERLEY-LIEB ALGEBRAS. NAGOYA MATHEMATICAL JOURNAL, 195, pp.125-152. https://doi.org/10.1017/S0027763000009740.
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Abstract We 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 . We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.
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