Following Lusztig, we consider a Coxeter group together with a weight function. Geck showed that the Kazhdan-Lusztig cells of are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of 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 are cells in the whole group, and we decompose the affine Weyl group of type into left and two-sided cells for a whole class of weight functions.
Suivant Lusztig, nous considérons un groupe de Coxeter 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 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 et nous décomposons le groupe de Weyl affine de type en cellules gauches et bilatères pour toute une classe de fonctions de poids.
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
@article{AIF_2009__59_4_1385_0, author = {Guilhot, J\'er\'emie}, title = {Generalized {Induction} of {Kazhdan-Lusztig} cells}, journal = {Annales de l'Institut Fourier}, pages = {1385--1412}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {59}, number = {4}, year = {2009}, doi = {10.5802/aif.2468}, mrnumber = {2566965}, zbl = {1186.20004}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2468/} }
TY - JOUR AU - Guilhot, Jérémie TI - Generalized Induction of Kazhdan-Lusztig cells JO - Annales de l'Institut Fourier PY - 2009 SP - 1385 EP - 1412 VL - 59 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2468/ DO - 10.5802/aif.2468 LA - en ID - AIF_2009__59_4_1385_0 ER -
%0 Journal Article %A Guilhot, Jérémie %T Generalized Induction of Kazhdan-Lusztig cells %J Annales de l'Institut Fourier %D 2009 %P 1385-1412 %V 59 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2468/ %R 10.5802/aif.2468 %G en %F AIF_2009__59_4_1385_0
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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