Generalized Induction of Kazhdan-Lusztig cells
Annales de l'Institut Fourier, Volume 59 (2009) no. 4, pp. 1385-1412.

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.

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.

DOI: 10.5802/aif.2468
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
Guilhot, Jérémie 1, 2

1 Aberdeen University Department of Mathematical Sciences King’s College Aberdeen AB24 3UE, Scotland (U.K.)
2 Université de Lyon 1 Institut Camille Jordan, CNRS UMR 5208 43 Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex (France)
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Guilhot, Jérémie. Generalized Induction of Kazhdan-Lusztig cells. Annales de l'Institut Fourier, Volume 59 (2009) no. 4, pp. 1385-1412. doi : 10.5802/aif.2468. https://aif.centre-mersenne.org/articles/10.5802/aif.2468/

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