|
Familles de caractères de groupes de réflexions complexes
Author(s):
Gunter
Malle;
Raphaël
Rouquier
Journal:
Represent. Theory
7
(2003),
610-640.
MSC (2000):
Primary 20C08;
Secondary 20C40
Posted:
November 20, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Nous étudions certains types de blocs d'algèbres de Hecke associées aux groupes de réflexions complexes qui généralisent les familles de caractères définies par Lusztig pour les groupes de Weyl. Nous déterminons ces blocs pour les groupes de réflexions spetsiaux et nous établissons un théorème de compatibilité entre familles et  -séries de Harish-Chandra.
References:
-
- 1.
- D. ALVIS ET G. LUSZTIG, The representations and generic degrees of the Hecke algebra of type
 , J. Reine Angew. Math. 336 (1982), 201-212. MR 84a:20013 - 2.
- D. BESSIS, Sur le corps de définition d'un groupe de réflexions complexe, Comm. in Algebra 25 (1997), 2703-2716. MR 98g:20017
- 3.
- M. BROUÉ ET S. KIM, Familles de caractères des algèbres de Hecke cyclotomiques, Advances in Math. 172 (2002), 53-136. MR 2003j:20006
- 4.
- M. BROUÉ ET G. MALLE, Zyklotomische Heckealgebren, Astérisque 212 (1993), 119-189. MR 94m:20095
- 5.
- M. BROUÉ ET G. MALLE, Generalized Harish-Chandra theory, in: Representations of reductive groups, Cambridge University Press, Cambridge, 1998, pp. 85-103. MR 2000k:20063
- 6.
- M. BROUÉ, G. MALLE ET J. MICHEL, Generic blocks of finite reductive groups, Astérisque 212 (1993), 7-92. MR 95d:20072
- 7.
- M. BROUÉ, G. MALLE ET J. MICHEL, Towards spetses I, Transform. Groups 4 (1999), 157-218. MR 2001b:20082
- 8.
- M. BROUÉ, G. MALLE ET R. ROUQUIER, Complex reflection groups, braid groups, Hecke algebras, J. Reine Angew. Math. 500 (1998), 127-190. MR 99m:20088
- 9.
- M. BROU´E ET J. MICHEL, Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne-Lusztig associées, in: M. Cabanes (ed.), Finite reductive groups, related structures and representations, Progress in Math. 141, Birkhäuser, 1997, pp. 73-139. MR 98h:20077
- 10.
- M. GECK, G. HISS, F. L¨UBECK, G. MALLE ET G. PFEIFFER, CHEVIE -- A system for computing and processing generic character tables. Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175-210. MR 99m:20017
- 11.
- M. GECK ET G. PFEIFFER, Characters of finite Coxeter groups and Iwahori-Hecke algebras, Oxford University Press, Oxford, 2000. MR 2002k:20017
- 12.
- M. GECK ET R. ROUQUIER, Centers and simple modules for Iwahori-Hecke algebras, in: M. Cabanes (ed.), Finite reductive groups, related structures and representations, Progress in Math. 141, Birkhäuser, 1997, pp. 251-272. MR 98c:20013
- 13.
- A. GYOJA, Cells and modular representations of Hecke algebras, Osaka J. Math. 33 (1996), 307-341. MR 97k:20018
- 14.
- G. LUSZTIG, A class of irreducible representations of a Weyl group. II, Indag. Math. 44 (1982), 219-226. MR 83h:20018
- 15.
- G. LUSZTIG, Characters of reductive groups over a finite field, Annals Math. Studies 107, Princeton University Press, Princeton, 1984. MR 86j:20038
- 16.
- G. LUSZTIG, Hecke algebras with unequal parameters, CRM Monographs, Amer. Math. Soc., Providence, 2003.
- 17.
- G. MALLE, Unipotente Grade imprimitiver komplexer Spiegelungsgruppen, J. Algebra 177 (1995), 768-826. MR 97a:20073
- 18.
- G. MALLE, Degrés relatifs des algèbres cyclotomiques associées aux groupes de réflexions complexes de dimension deux, in: M. Cabanes (ed.), Finite reductive groups, related structures and representations, Progress in Math. 141, Birkhäuser, 1997, pp. 311-332. MR 98h:20019
- 19.
- G. MALLE, Spetses, Doc. Math. J. DMV Extra Volume ICM II (1998), 87-96. MR 99m:20090
- 20.
- G. MALLE, On the rationality and fake degrees of characters of cyclotomic algebras, J. Fac. Sci. Univ. Tokyo 6 (1999), 647-677. MR 2001e:20008
- 21.
- G. MALLE, On the generic degrees of cyclotomic algebras, Represent. Theory 4 (2000), 342-369. MR 2002a:20005
- 22.
- R. ROUQUIER, Familles et blocs d'algèbres de Hecke, C. R. Acad. Sci. Sér. I Math. Paris 329 (1999), 1037-1042. MR 2001f:20012
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2000):
20C08,
20C40
Retrieve articles in all Journals with MSC
(2000):
20C08,
20C40
Additional Information:
Gunter
Malle
Affiliation:
Fachbereich Mathematik/Informatik, Universität
Kassel, Heinrich-Plett-Str. 40, D--34132 Kassel,
Germany
Email:
malle@mathematik.uni-kassel.de
Raphaël
Rouquier
Affiliation:
UMR 7586 du CNRS et UFR de Mathématiques,
Université Denis Diderot, Case 7012,
2 Place Jussieu, F--75251 Paris Cedex 05, France
Email:
rouquier@math.jussieu.fr
DOI:
10.1090/S1088-4165-03-00193-6
PII:
S 1088-4165(03)00193-6
Received by editor(s):
April 8, 2003
Received by editor(s) in revised form:
October 2, 2003
Posted:
November 20, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org