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

Author: Jian-yi Shi
Journal: Proc. Amer. Math. Soc. 133 (2005), 2525-2531
MSC (2000): Primary 20F55, 05E15
Published electronically: March 22, 2005
MathSciNet review: 2146194
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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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Additional Information

Jian-yi Shi
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China – and – Center for Combinatorics, Nankai University, Tianjin, 300071, People’s Republic of China
MR Author ID: 231063

Received by editor(s): March 28, 2004
Received by editor(s) in revised form: April 14, 2004, May 1, 2004, and May 5, 2004
Published electronically: March 22, 2005
Additional Notes: This work was supported by Nankai University, the 973 Project of MST of China, the NSF of China, the SF of the University Doctoral Program of ME of China, the Shanghai Priority Academic Discipline, and the CST of Shanghai
Communicated by: John R. Stembridge
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.