Generic character sheaves on disconnected groups and character values
Author:
G. Lusztig
Journal:
Represent. Theory 12 (2008), 225-235
MSC (2000):
Primary 20G99
DOI:
https://doi.org/10.1090/S1088-4165-08-00327-0
Published electronically:
April 17, 2008
MathSciNet review:
2403560
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We relate a generic character sheaf on a disconnected reductive group with a character of the rational points of the group over a finite field extending a known result in the connected case.
- P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161. MR 393266, DOI https://doi.org/10.2307/1971021
- François Digne and Jean Michel, Groupes réductifs non connexes, Ann. Sci. École Norm. Sup. (4) 27 (1994), no. 3, 345–406 (French, with English and French summaries). MR 1272294
- George Lusztig, Green functions and character sheaves, Ann. of Math. (2) 131 (1990), no. 2, 355–408. MR 1043271, DOI https://doi.org/10.2307/1971496
- G. Lusztig, Remarks on computing irreducible characters, J. Amer. Math. Soc. 5 (1992), no. 4, 971–986. MR 1157292, DOI https://doi.org/10.1090/S0894-0347-1992-1157292-7
- G. Lusztig, Character sheaves on disconnected groups. I, Represent. Theory 7 (2003), 374–403. MR 2017063, DOI https://doi.org/10.1090/S1088-4165-03-00204-8
- Gunter Malle, Generalized Deligne-Lusztig characters, J. Algebra 159 (1993), no. 1, 64–97. MR 1231204, DOI https://doi.org/10.1006/jabr.1993.1147
- Toshiaki Shoji, Character sheaves and almost characters of reductive groups. I, II, Adv. Math. 111 (1995), no. 2, 244–313, 314–354. MR 1318530, DOI https://doi.org/10.1006/aima.1995.1024
- J.-L. Waldspurger, Le groupe ${\rm GL}_N$ tordu, sur un corps fini, Nagoya Math. J. 182 (2006), 313–379 (French, with English summary). MR 2235346, DOI https://doi.org/10.1017/S002776300002691X
Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20G99
Retrieve articles in all journals with MSC (2000): 20G99
Additional Information
G. Lusztig
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID:
117100
Email:
gyuri@math.mit.edu
Received by editor(s):
April 7, 2007
Published electronically:
April 17, 2008
Additional Notes:
Supported in part by the National Science Foundation.
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.