Generalized Jones traces and Kazhdan--Lusztig bases

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We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the positivity of certain structure constants for the associated Kazhdan--Lusztig basis. We also explore some consequences of the existence of a Jones-type trace on the Hecke algebra of a Coxeter group, such as simple procedures for computing leading terms of certain Kazhdan--Lusztig polynomials. The sequel to this paper is math.QA/0509363.
Approximately 58 pages, AMSTeX, one figure. Revised in light of referee comments

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Quantum Algebra, Combinatorics, 20C08

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http://salesiana.dossiersoluciones.com/handle/123456789/126791

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509362
 http://arxiv.org/abs/math/0509362

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arXiv