Classification of Coxeter groups with finitely many elements of <strong>a</strong>-value 2

Green, R. M.; Xu, Tianyuan

doi:10.5802/alco.95

Classification of Coxeter groups with finitely many elements of a-value 2

Green, R. M.¹; Xu, Tianyuan ²

¹ Department of Mathematics University of Colorado Boulder, Campus Box 395 Boulder, Colorado USA, 80309
² Department of Mathematics and Statistics Queen’s University Kingston, Ontario Canada, K7L 3N6

Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 331-364.

Abstract

We consider Lusztig’s $a$ -function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of $a$ -value 2 in terms of Coxeter diagrams.

Received: 2018-05-22
Revised: 2019-07-10
Accepted: 2019-09-14
Published online: 2020-04-01

DOI: 10.5802/alco.95

Classification: 05E10, 20C08
Keywords: Coxeter groups, Hecke algebras, Lusztig’s $\mathbf{a}$-function, fully commutative elements, heaps, star operations

Author's affiliations:

Green, R. M. ¹; Xu, Tianyuan ²

¹ Department of Mathematics University of Colorado Boulder, Campus Box 395 Boulder, Colorado USA, 80309
² Department of Mathematics and Statistics Queen’s University Kingston, Ontario Canada, K7L 3N6

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Green, R. M. and Xu, Tianyuan},
     title = {Classification of {Coxeter} groups with finitely many elements of <strong>a</strong>-value 2},
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Green, R. M.; Xu, Tianyuan. Classification of Coxeter groups with finitely many elements of a-value 2. Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 331-364. doi : 10.5802/alco.95. https://alco.centre-mersenne.org/articles/10.5802/alco.95/

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