Generalized induction of Kazhdan-Lusztig cells

Details Generalized induction of Kazhdan-Lusztig cells Generalized induction of Kazhdan-Lusztig cells

2008-02-11

arxiv.org/abs/0802.1408v3

Mathematics

Representation Theory

21 pages, 3 figures

Scientific paper

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.

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