Generalized Induction of Kazhdan-Lusztig cells

Guilhot, Jérémie

Generalized Induction of Kazhdan-Lusztig cells
[Induction généralisée des cellules de Kazhdan-Lusztig]

Annales de l'Institut Fourier, Tome 59 (2009), p. 1385-1412 / Harvested from Numdam

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Résumé
Abstract

Suivant Lusztig, nous considérons un groupe de Coxeter $W$ avec une fonction de poids. Geck a montré que les cellules de Kazhdan-Lusztig sont compatibles avec les sous-groupes paraboliques. Dans cet article nous généralisons cet argument à des sous-ensembles de $W$ qui ne sont pas forcément des sous-groupes paraboliques. Nous obtenons deux applications : nous montrons que sous certaines hypothèses sur les paramètres les cellules de certains sous-groupes paraboliques sont aussi des cellules de $W$ et nous décomposons le groupe de Weyl affine de type $G$ en cellules gauches et bilatères pour toute une classe de fonctions de poids.

Following Lusztig, we consider a Coxeter group $W$ together with a weight function. Geck showed that the Kazhdan-Lusztig cells of $W$ are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of $W$ which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of certain parabolic subgroups of $W$ are cells in the whole group, and we decompose the affine Weyl group of type $G$ into left and two-sided cells for a whole class of weight functions.

Publié le : 2009-01-01

MR 2566965 | Zbl 1186.20004

DOI : https://doi.org/10.5802/aif.2468
Classification: 20C08
Mots clés: groupes de Coxeter, Groupes de Weyl affines, Algèbre de Hecke, Cellules de Kazhdan-Lusztig, Paramètres inégaux

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     author = {Guilhot, J\'er\'emie},
     title = {Generalized Induction of Kazhdan-Lusztig cells},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
     pages = {1385-1412},
     doi = {10.5802/aif.2468},
     zbl = {1186.20004},
     mrnumber = {2566965},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_4_1385_0}
}

Guilhot, Jérémie. Generalized Induction of Kazhdan-Lusztig cells. Annales de l'Institut Fourier, Tome 59 (2009) pp. 1385-1412. doi : 10.5802/aif.2468. http://gdmltest.u-ga.fr/item/AIF_2009__59_4_1385_0/

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