ALGEBRAIC COMBINATORICS

no. 3
Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter systems
Green, R. M.1; Xu, Tianyuan2
1 Department of Mathematics University of Colorado Boulder Boulder, CO, USA
2 Department of Mathematics and Statistics Haverford College Haverford, PA, USA
Algebraic Combinatorics, Volume 6 (2023) no. 3, pp. 727-772.

A Coxeter group is said to be a(2)-finite if it has finitely many elements of a-value (in the sense of Lusztig) equal to 2. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided Kazhdan–Lusztig cells of a-value 2 in an irreducible a(2)-finite Coxeter group. In particular, we introduce elements we call stubs to parameterize the one-sided cells and we characterize the one-sided cells via both star operations and weak Bruhat orders. We also compute the cardinalities of all the one-sided and two-sided cells of a-value 2 in irreducible a(2)-finite Coxeter groups.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.275
Classification: 20F55, 20C08
Keywords: Kazhdan–Lusztig cells, Lusztig’s $\mathbf{a}$-function, Coxeter groups, fully commutative elements, heaps, star operations
Green, R. M. 1; Xu, Tianyuan 2

1 Department of Mathematics University of Colorado Boulder Boulder, CO, USA
2 Department of Mathematics and Statistics Haverford College Haverford, PA, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Green, R. M.; Xu, Tianyuan. Kazhdan–Lusztig cells of $\protect \mathbf{a}$-value 2 in $\protect \mathbf{a}(2)$-finite Coxeter systems. Algebraic Combinatorics, Volume 6 (2023) no. 3, pp. 727-772. doi : 10.5802/alco.275. https://alco.centre-mersenne.org/articles/10.5802/alco.275/

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