1 F eb 2 00 1 FULLY COMMUTATIVE KAZHDAN – LUSZTIG CELLS
نویسندگان
چکیده
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 types de cellules de Kazhdan–Lusztig, en utilisant une base canonique pour une version généralisée de l'algèbre de Temperley– Lieb.
منابع مشابه
Leading coefficients of Kazhdan–Lusztig polynomials and fully commutative elements
Let W be a Coxeter group of type ̃ An−1. We show that the leading coefficient, μ(x,w), of the Kazhdan–Lusztig polynomial Px,w is always equal to 0 or 1 if x is fully commutative (and w is arbitrary).
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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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