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

Shi, Jian-yi

doi:10.1090/S0002-9939-03-06930-2

Fully commutative elements and Kazhdan–Lusztig cells in the finite and affine Coxeter groups
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by Jian-yi Shi

Proc. Amer. Math. Soc. 131 (2003), 3371-3378

DOI: https://doi.org/10.1090/S0002-9939-03-06930-2

Published electronically: February 24, 2003

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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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