Proceedings of the American Mathematical Society

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

Author(s): Jian-yi Shi
Journal: Proc. Amer. Math. Soc. 133 (2005), 2525-2531.
MSC (2000): Primary 20F55, 05E15
Posted: March 22, 2005
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Abstract: Let

be an irreducible finite or affine Coxeter group and let $W_{\mathrm{c}}$ be the set of fully commutative elements in

. 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

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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

DOI: 10.1090/S0002-9939-05-07834-2
PII: S 0002-9939(05)07834-2
Received by editor(s): March 28, 2004
Received by editor(s) in revised form: April 14, 2004, May 1, 2004, and May 5, 2004
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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