Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups, II

Shi, Jian-yi

doi:10.1090/S0002-9939-05-07834-2

Fully commutative elements and Kazhdan-Lusztig cells in the finite and affine Coxeter groups, II
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Proc. Amer. Math. Soc. 133 (2005), 2525-2531 Request permission

Abstract:

Let $W$ be an irreducible finite or affine Coxeter group and let $W_{\mathrm {c}}$ be the set of fully commutative elements in $W$. We prove that the set $W_{\mathrm {c}}$ is closed under the Kazhdan-Lusztig preorder ${\underset {{LR}}{\geqslant }}$ if and only if $W_{\mathrm {c}}$ is a union of two-sided cells of $W$.

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