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

Author: Jian-yi Shi
Journal: Proc. Amer. Math. Soc. 131 (2003), 3371-3378
MSC (2000): Primary 20F55, 05E15
Published electronically: February 24, 2003
MathSciNet review: 1990625
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Abstract | References | Similar Articles | Additional Information

Abstract: The main goal of the paper is to show that the fully commutative elements in the affine Coxeter group $\widetilde {C}_{n}$ form a union of two-sided cells. Then we completely answer the question of when the fully commutative elements of $W$ form or do not form a union of two-sided cells in the case where $W$ is either a finite or an affine Coxeter group.

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Additional Information

Jian-yi Shi
Affiliation: Center for Combinatorics, The Key Laboratory of Pure Mathematics and Combinatorics of Ministry of Education, Nankai University, Tianjin, 300071, People’s Republic of China – and – Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China

Received by editor(s): May 1, 2002
Received by editor(s) in revised form: May 28, 2002, and June 13, 2002
Published electronically: February 24, 2003
Additional Notes: The author was partially supported by Nankai University, the 973 Project of MST of China, the NSF of China, the SF of the University Doctorial Program of ME of China and the Shanghai Priority Academic Discipline
Communicated by: John R. Stembridge
Article copyright: © Copyright 2003 American Mathematical Society