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2009 Commuting families in Hecke and Temperley-Lieb algebras
Tom Halverson, Manuela Mazzocco, Arun Ram
Nagoya Math. J. 195(none): 125-152 (2009).

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 $U_{h}\mathfrak{gl}_{n}$. We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.

Citation

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Tom Halverson. Manuela Mazzocco. Arun Ram. "Commuting families in Hecke and Temperley-Lieb algebras." Nagoya Math. J. 195 125 - 152, 2009.

Information

Published: 2009
First available in Project Euclid: 14 September 2009

zbMATH: 1217.20002
MathSciNet: MR2552957

Subjects:
Primary: 20G05
Secondary: 16G99, 81R50, 82B20

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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Vol.195 • 2009
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