Fully commutative Kazhdan-Lusztig cells
[Cellules pleinement commutatives de Kazhdan-Lusztig]
Green, Richard M.1 ; Losonczy, Jozsef2
1 Lancaster University, Department of Mathematics and Statistics, Lancaster LA1 4YF (Grande-Bretagne)
2 Long Island University, Department of Mathematics, Brookville, NY 11548 (USA)
Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1025-1045.

Nous étudions la compatibilité entre l'ensemble des éléments pleinement commutatifs d'un groupe de Coxeter et les divers types de cellules de Kazhdan-Lusztig, en utilisant une base canonique pour une version généralisée de l'algèbre de Temperley-Lieb.

We investigate the compatibility of the set of fully commutative elements of a Coxeter group with the various types of Kazhdan-Lusztig cells using a canonical basis for a generalized version of the Temperley-Lieb algebra.

DOI : 10.5802/aif.1843
Classification : 20C08, 20F55
Keywords: canonical basis, cell theory, Coxeter group, Hecke algebra, Kazhdan-Lusztig basis, Temperley-Lieb algebra
Mot clés : base canonique, théorie des cellules, groupe de Coxeter, algèbre de Hecke, base de Kazhdan-Lusztig, algèbre de Temperley-Lieb
Green, Richard M. 1 ; Losonczy, Jozsef 2

1 Lancaster University, Department of Mathematics and Statistics, Lancaster LA1 4YF (Grande-Bretagne)
2 Long Island University, Department of Mathematics, Brookville, NY 11548 (USA) 
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     title = {Fully commutative {Kazhdan-Lusztig} cells},
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Green, Richard M.; Losonczy, Jozsef. Fully commutative Kazhdan-Lusztig cells. Annales de l'Institut Fourier, Tome 51 (2001) no. 4, pp. 1025-1045. doi : 10.5802/aif.1843. http://www.numdam.org/articles/10.5802/aif.1843/

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