|
On the existence of a unipotent support for the irreducible characters of a finite group of Lie type
Author(s):
Meinolf
Geck;
Gunter
Malle
Journal:
Trans. Amer. Math. Soc.
352
(2000),
429-456.
MSC (1991):
Primary 20C33, 20G40
Posted:
September 21, 1999
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite group of Lie type. This problem was solved by Lusztig in the case where the characteristic of the field over which the group is defined is large enough. The first named author extended this to the case where the characteristic is good. It is the purpose of this paper to remove this condition as well, so that the existence of unipotent supports is established in complete generality.
References:
- [1]
- D.I. Deriziotis, On the number of conjugacy classes in finite groups of Lie type, Comm. in Algebra 13 (1985), 1019-1045. MR 86i:20067
- [2]
- M. Geck, On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes, Documenta Math. 1 (1996), 293-317. (electronic) MR 98c:20084
- [3]
- M. Geck and G. Malle, Cuspidal unipotent classes and cuspidal Brauer characters, J. London Math. Soc. 53 (1996), 63-78. MR 97b:20013
- [4]
- G. Laumon, Faisceaux caractères, Séminaire Bourbaki No. 709, Astérisque 177-178 (1989), 231-260. MR 91m:20062
- [5]
- G. Lusztig, On the finiteness of the number of unipotent classes, Invent. Math. 34 (1976), 201-213. MR 54:7653
- [6]
- G. Lusztig, Some problems in the representation theory of finite Chevalley groups, Proc. Symp. Pure Math., vol. 37, Amer. Math. Soc., Providence, 1980, pp. 313-317. MR 82i:20014
- [7]
- G. Lusztig, Characters of reductive groups over a finite field, Ann. Math. Studies, vol. 107, Princeton U. Press, Princeton, 1984. MR 86j:20038
- [8]
- G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), 205-272. MR 86d:20050
- [9]
- G. Lusztig, Character sheaves IV, Advances in Math. 59 (1986), 1-63. MR 87m:20118b
- [10]
- G. Lusztig, Character sheaves V, Advances in Math. 61 (1986), 103-155. MR 87m:20118c
- [11]
- G. Lusztig, On the representations of reductive groups with disconnected centre, Orbites Unipotentes et Représentations, I. Groupes Finis et Algèbres de Hecke, Astérisque 168 (1988), 157-166. MR 90j:20083
- [12]
- G. Lusztig, A unipotent support for irreducible representations, Advances in Math. 94 (1992), 139-179. MR 94a:20073
- [13]
- G. Lusztig and N. Spaltenstein, Induced unipotent classes, J. London Math. Soc. 19 (1979), 41-52. MR 82g:20070
- [14]
- G. Lusztig and N. Spaltenstein, On the generalized Springer correspondence for classical groups, Algebraic groups and related topics, Advanced Studies in Pure Math., vol. 6, Kinokuniya and North-Holland, Tokyo and Amsterdam, 1985, pp. 289-316. MR 87g:20072a
- [15]
- G. Malle, Die unipotenten Charaktere von
 , Comm. Algebra 18 (1990), 2361-2381. MR 91k:20015 - [16]
- T. Shoji, Green functions of reductive groups over a finite field, Proc. Symp. Pure Math., vol. 47, Amer. Math. Soc., Providence, 1987, pp. 289-302. MR 88m:20014
- [17]
- T. Shoji, Character sheaves and almost characters of reductive groups, II, Advances in Math. 111 (1995), 314-354. MR 95k:20069
- [18]
- T. Shoji, Unipotent characters of finite classical groups, Finite Reductive Groups, Related Structures and Representations (M. Cabanes, ed.), Progress in Math., vol. 141, Birkhäuser, Boston, 1997, pp. 373-413. MR 98h:20079
- [19]
- N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Math., vol. 946, Springer, Berlin Heidelberg New York, 1982. MR 84a:14024
- [20]
- N. Spaltenstein, On the generalized Springer correspondence for exceptional groups, Algebraic groups and related topics, Advanced Studies in Pure Math., vol. 6, Kinokuniya and North-Holland, Tokyo and Amsterdam, 1985, pp. 317-338. MR 87g:20072b
- [21]
- M. Suzuki, On a class of doubly transitive groups, Ann. of Math. 75 (1962), 105-145. MR 25:112
- [22]
- H.N. Ward, On Ree's series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62-89. MR 33:5752
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
20C33, 20G40
Retrieve articles in all Journals with MSC
(1991):
20C33, 20G40
Additional Information:
Meinolf
Geck
Affiliation:
U.F.R. de Mathématiques, Université Paris 7, et UMR 7586 du CNRS, 2 Place Jussieu, F--75251 Paris Cedex 05, France
Address at time of publication:
Institut Girard Desargues, Université Lyon 1, 69622 Villeurbanne Cedex, France
Email:
geck@desargues.univ-lyon1.fr
Gunter
Malle
Affiliation:
I.W.R., Im Neuenheimer Feld 368, D--69120 Heidelberg, Germany
Address at time of publication:
FB Mathematik/Informatik, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
Email:
malle@mathematik.uni-kassel.de
DOI:
10.1090/S0002-9947-99-02210-2
PII:
S 0002-9947(99)02210-2
Received by editor(s):
November 1, 1996
Received by editor(s) in revised form:
July 29, 1997
Posted:
September 21, 1999
Additional Notes:
The second author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft
Copyright of article:
Copyright
1999,
American Mathematical Society
|
Comments: webmaster@ams.org