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Jérémie Guilhot
Generalized Induction of Kazhdan-Lusztig cells
(Induction généralisée des cellules de Kazhdan-Lusztig)
Annales de l'institut Fourier, 59 no. 4 (2009), p. 1385-1412, doi: 10.5802/aif.2468
Article PDF | Reviews MR 2566965 | Zbl 1186.20004
Class. Math.: 20C08
Keywords: Coxeter groups, Affine Weyl groups, Hecke algebras, Kazhdan-Lusztig cells, Unequal parameters

Résumé - Abstract

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.

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