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Zbl 1008.20036
Green, Richard M.; Losonczy, Jozsef
Fully commutative Kazhdan-Lusztig cells. (English)
[J] Ann. Inst. Fourier 51, No.4, 1025-1045 (2001). ISSN 0373-0956; ISSN 1777-5310/e

Let $W$ be a Coxeter group. An element $w$ of $W$ is fully commutative if any two reduced expressions of $w$ can be obtained from each other by a sequence of interchanges of adjacent, commuting Coxeter generators. Let $W_c$ be the set of fully commutative elements of $W$. Then the main result of the paper is to show that when $W$ is of type $B_n$, the set $W_c$ is a union of two-sided Kazhdan-Lusztig cells of $W$. Furthermore, the authors show that in an irreducible finite Coxeter group $W$, the set $W_c$ forms a union of two-sided Kazhdan-Lusztig cells if and only if $W$ has no standard parabolic subgroup of type $D_4$.
[Shi Jian-yi (Shanghai)]

MSC 2000:: *20F55 Coxeter groups
20C08 Hecke algebras and their representations

Keywords: Hecke algebras; Coxeter groups; Kazhdan-Lusztig cells; fully commutative elements

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