Generalized Induction of Kazhdan-Lusztig cells

Guilhot, Jérémie

Annales de l'Institut Fourier, Tome 59 (2009) no. 4, pp. 1385-1412.

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.

Classification : 20C08
Keywords: Coxeter groups, Affine Weyl groups, Hecke algebras, Kazhdan-Lusztig cells, Unequal parameters
Mot clés : groupes de Coxeter, Groupes de Weyl affines, Algèbre de Hecke, Cellules de Kazhdan-Lusztig, Paramètres inégaux

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