2 00 7 Generalized Jones Traces and Kazhdan – Lusztig Bases
نویسنده
چکیده
We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the pos-itivity 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.
منابع مشابه
Se p 20 05 GENERALIZED JONES TRACES AND KAZHDAN – LUSZTIG BASES
We develop some applications of certain algebraic and combinatorial conditions on the elements of Coxeter groups, such as elementary proofs of the pos-itivity 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 ter...
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We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan–Lusztig cells using a canonical basis for a generalized version of the Temperley–Lieb algebra. Cellules pleinement commutatives de Kazhdan–Lusztig Nousétudions la compatibilité entre l'ensemble deséléments pleinement commu-tatifs d'un groupe de Coxeter et les divers typ...
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General facts of linear algebra are used to give proofs for the (wellknown) existence of analogs of Kazhdan-Lusztig polynomials corresponding to formal analogs of the Kazhdan-Lusztig involution, and of explicit formulae (some new, some known) for their coefficients in terms of coefficients of other natural families of polynomials (such as the corresponding formal analogs of the Kazhdan-Lusztig ...
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In this paper we compute the leading coefficients μ(y,w) of the Kazhdan-Lusztig polynomials Py,w for an affineWeyl group of type B̃2. When a(y) ≤ a(w) or a(y) = 2 and a(w) = 1, we compute all μ(y,w) clearly, where a(y) is the a-function of a Coxeter group defined by Lusztig (see [L1]). With these values μ(y,w), we are able to show that a conjecture of Lusztig on distinguished involutions is true...
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