Jeremie Guilhot
Published 2008-02-11, updated 2008-10-28Version 3
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 a certain finite parabolic subgroup of $W$ are cells in the whole group, and we decompose the affine Weyl group $\tilde{G}_{2}$ into left and two-sided cells for a whole class of weight functions.
Comments: 21 pages, 3 figures
On the determination of Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters
Infinite Reduced Words, Lattice Property And Braid Graph of Affine Weyl Groups
On tensor categories attached to cells in affine Weyl groups
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