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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: subscription required (your ip address: 50.16.166.175) | Reviews MR 2566965 | Zbl 1186.20004
Class. Math.: 20C08
Keywords: Coxeter groups, Affine Weyl groups, Hecke algebras, Kazhdan-Lusztig cells, Unequal parameters
[1] R. Bedard, “Cells for two Coxeter groups”, Comm. Algebra 14 (1986), p. 1253-1286
Article | MR 842039 | Zbl 0608.20037
[2] K. Bremke, “On generalized cells in affine Weyl groups”, Journal of Algebra 191 (1997), p. 149-173
Article | MR 1444494 | Zbl 0942.20019
[3] C. Chen, “The decomposition into left cells of the affine Weyl group of type $\tilde{D}_{4}$”, Journal of Algebra 163 (1994), p. 692-728
Article | MR 1265858 | Zbl 0799.20039
[4] F. Du Cloux, “An abstract model for Bruhat intervals”, European J. Combin. 21 (2000), p. 197-222
Article | MR 1742435 | Zbl 0953.05083
[5] J. Du, “The decomposition into cells of the affine Weyl group of type $\tilde{B}_{3}$”, Comm. Algebra 16 (1988), p. 1383-1409
Article | MR 941176 | Zbl 0644.20030
[6] M. Geck, “On the induction of Kazhdan-Lusztig cells”, Bull. London Math. Soc. 35 (2003) no. 5, p. 608-614
Article | MR 1989489 | Zbl 1045.20004
[7] J. Guilhot, “On the determination of Kazhdan-Lusztig cells for affine Weyl group with unequal parameters”, Journal of Algebra 318 (2007), p. 893-917
Article | MR 2371977 | Zbl 1146.20033
[8] J. Guilhot, “Computations in Generalized induction of Kazhdan-Lusztig cells”, available at http://arxiv.org/abs/0810.5165, 2008
arXiv
[9] J. Guilhot, “On the lowest two-sided cell in affine Weyl groups”, Represent. Theory 12 (2008), p. 327-345
Article | MR 2448287 | Zbl pre05526473
[10] D. A. Kazhdan & G. Lusztig, “Schubert varieties and Poincaré duality”, Proc. Sympos. Pure Math. 36 (1980), p. 185-203, Amer. Math. Soc. MR 573434 | Zbl 0461.14015
[11] G. Lusztig, “Hecke algebras and Jantzen’s generic decomposition patterns”, Advances in Mathematics 37 (1980), p. 121-164
Article | MR 591724 | Zbl 0448.20039
[12] G. Lusztig, “Cells in affine Weyl groups”, Advanced Studies in Pure Math. 6 (1985), p. 255-287 MR 803338 | Zbl 0569.20032
[13] G. Lusztig, “The two-sided cells of the affine Weyl group of type $\tilde{A}_{n}$”, Math. Sci. Res. Inst. Publ 4 (1985), p. 275-283
Article | MR 823323 | Zbl 0602.20037
[14] G. Lusztig, Hecke algebras with unequal parameters 18, CRM Monographs Ser., 2003, Amer. Math. Soc. , Providence, RI MR 1974442 | Zbl 1051.20003
[15] Martin Schönert & , GAP – Groups, Algorithms, and Programming – version 3 release 4 patchlevel 4, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1997
[16] J.-Y. Shi, The Kazhdan-Lusztig cells in certain affine Weyl groups, Lectures Notes in Math. 1179, Springer-Verlag, 1986 MR 835214 | Zbl 0582.20030
[17] J.-Y. Shi, “Left cells in affine Weyl group ${W}_{a}(\tilde{D}_{4})$”, Osaka J. Math. 31 (1994), p. 27-50
Article | MR 1262787 | Zbl 0816.20040
[18] J.-Y. Shi, “Left cells in affine Weyl groups”, Tokohu Math. J. 46 (1994), p. 105-124
Article | MR 1256730 | Zbl 0798.20040
[19] N. Xi, Representations of affine Hecke algebras, Lectures Notes in Math. 1587, Springer-Verlag, 1994 MR 1320509 | Zbl 0817.20051
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: subscription required (your ip address: 50.16.166.175) | 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.
Bibliography
Article | MR 842039 | Zbl 0608.20037
[2] K. Bremke, “On generalized cells in affine Weyl groups”, Journal of Algebra 191 (1997), p. 149-173
Article | MR 1444494 | Zbl 0942.20019
[3] C. Chen, “The decomposition into left cells of the affine Weyl group of type $\tilde{D}_{4}$”, Journal of Algebra 163 (1994), p. 692-728
Article | MR 1265858 | Zbl 0799.20039
[4] F. Du Cloux, “An abstract model for Bruhat intervals”, European J. Combin. 21 (2000), p. 197-222
Article | MR 1742435 | Zbl 0953.05083
[5] J. Du, “The decomposition into cells of the affine Weyl group of type $\tilde{B}_{3}$”, Comm. Algebra 16 (1988), p. 1383-1409
Article | MR 941176 | Zbl 0644.20030
[6] M. Geck, “On the induction of Kazhdan-Lusztig cells”, Bull. London Math. Soc. 35 (2003) no. 5, p. 608-614
Article | MR 1989489 | Zbl 1045.20004
[7] J. Guilhot, “On the determination of Kazhdan-Lusztig cells for affine Weyl group with unequal parameters”, Journal of Algebra 318 (2007), p. 893-917
Article | MR 2371977 | Zbl 1146.20033
[8] J. Guilhot, “Computations in Generalized induction of Kazhdan-Lusztig cells”, available at http://arxiv.org/abs/0810.5165, 2008
arXiv
[9] J. Guilhot, “On the lowest two-sided cell in affine Weyl groups”, Represent. Theory 12 (2008), p. 327-345
Article | MR 2448287 | Zbl pre05526473
[10] D. A. Kazhdan & G. Lusztig, “Schubert varieties and Poincaré duality”, Proc. Sympos. Pure Math. 36 (1980), p. 185-203, Amer. Math. Soc. MR 573434 | Zbl 0461.14015
[11] G. Lusztig, “Hecke algebras and Jantzen’s generic decomposition patterns”, Advances in Mathematics 37 (1980), p. 121-164
Article | MR 591724 | Zbl 0448.20039
[12] G. Lusztig, “Cells in affine Weyl groups”, Advanced Studies in Pure Math. 6 (1985), p. 255-287 MR 803338 | Zbl 0569.20032
[13] G. Lusztig, “The two-sided cells of the affine Weyl group of type $\tilde{A}_{n}$”, Math. Sci. Res. Inst. Publ 4 (1985), p. 275-283
Article | MR 823323 | Zbl 0602.20037
[14] G. Lusztig, Hecke algebras with unequal parameters 18, CRM Monographs Ser., 2003, Amer. Math. Soc. , Providence, RI MR 1974442 | Zbl 1051.20003
[15] Martin Schönert & , GAP – Groups, Algorithms, and Programming – version 3 release 4 patchlevel 4, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1997
[16] J.-Y. Shi, The Kazhdan-Lusztig cells in certain affine Weyl groups, Lectures Notes in Math. 1179, Springer-Verlag, 1986 MR 835214 | Zbl 0582.20030
[17] J.-Y. Shi, “Left cells in affine Weyl group ${W}_{a}(\tilde{D}_{4})$”, Osaka J. Math. 31 (1994), p. 27-50
Article | MR 1262787 | Zbl 0816.20040
[18] J.-Y. Shi, “Left cells in affine Weyl groups”, Tokohu Math. J. 46 (1994), p. 105-124
Article | MR 1256730 | Zbl 0798.20040
[19] N. Xi, Representations of affine Hecke algebras, Lectures Notes in Math. 1587, Springer-Verlag, 1994 MR 1320509 | Zbl 0817.20051
© Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310