Generalized Induction of Kazhdan-Lusztig cells

Jérémie Guilhot[1]

  • [1] Aberdeen University Department of Mathematical Sciences King’s College Aberdeen AB24 3UE, Scotland (U.K.) Université de Lyon 1 Institut Camille Jordan, CNRS UMR 5208 43 Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex (France)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 4, page 1385-1412
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Guilhot, Jérémie. "Generalized Induction of Kazhdan-Lusztig cells." Annales de l’institut Fourier 59.4 (2009): 1385-1412. <http://eudml.org/doc/10432>.

@article{Guilhot2009,
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.},
affiliation = {Aberdeen University Department of Mathematical Sciences King’s College Aberdeen AB24 3UE, Scotland (U.K.) Université de Lyon 1 Institut Camille Jordan, CNRS UMR 5208 43 Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex (France)},
author = {Guilhot, Jérémie},
journal = {Annales de l’institut Fourier},
keywords = {Coxeter groups; Affine Weyl groups; Hecke algebras; Kazhdan-Lusztig cells; Unequal parameters; affine Weyl groups; weight functions; unions of left cells; parabolic subgroups; generalized induction},
language = {eng},
number = {4},
pages = {1385-1412},
publisher = {Association des Annales de l’institut Fourier},
title = {Generalized Induction of Kazhdan-Lusztig cells},
url = {http://eudml.org/doc/10432},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Guilhot, Jérémie
TI - Generalized Induction of Kazhdan-Lusztig cells
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 4
SP - 1385
EP - 1412
AB - 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.
LA - eng
KW - Coxeter groups; Affine Weyl groups; Hecke algebras; Kazhdan-Lusztig cells; Unequal parameters; affine Weyl groups; weight functions; unions of left cells; parabolic subgroups; generalized induction
UR - http://eudml.org/doc/10432
ER -

References

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  14. G. Lusztig, Hecke algebras with unequal parameters, 18 (2003), CRM Monographs Ser. Zbl1051.20003MR1974442
  15. Martin Schönert, GAP – Groups, Algorithms, and Programming – version 3 release 4 patchlevel 4, (1997), Aachen, Germany 
  16. J.-Y. Shi, The Kazhdan-Lusztig cells in certain affine Weyl groups, 1179 (1986), Springer-Verlag Zbl0582.20030MR835214
  17. J.-Y. Shi, Left cells in affine Weyl group W a ( D ˜ 4 ) , Osaka J. Math. 31 (1994), 27-50 Zbl0816.20040MR1262787
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