Commuting families in Hecke and Temperley-Lieb Algebras
نویسندگان
چکیده
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 Uhgln. We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.
منابع مشابه
Representations of Temperley–lieb Algebras
We define a commuting family of operators T0, T1, . . . , Tn in the Temperley– Lieb algebra An(x) of type An−1. Using an appropriate analogue to Murphy basis of the Iwahori–Hecke algebra of the symmetric group, we describe the eigenvalues arising from the triangular action of the said operators on the cell modules of An(x). These results are used to provide the Temperley–Lieb algebras of type A...
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