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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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


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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2525-2531
  • MSC (2000): Primary 20F55, 05E15
  • DOI:
  • MathSciNet review: 2146194