Generalized Induction of Kazhdan-Lusztig cells
Annales de l'Institut Fourier, Volume 59 (2009) no. 4, p. 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 : https://doi.org/10.5802/aif.2468
Classification:  20C08
Keywords: Coxeter groups, Affine Weyl groups, Hecke algebras, Kazhdan-Lusztig cells, Unequal parameters
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {4},
     year = {2009},
     pages = {1385-1412},
     doi = {10.5802/aif.2468},
     mrnumber = {2566965},
     zbl = {1186.20004},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_2009__59_4_1385_0/

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