A class of perverse sheaves on a partial flag manifold
Author:
G. Lusztig
Journal:
Represent. Theory 11 (2007), 122-171
MSC (2000):
Primary 20G99
DOI:
https://doi.org/10.1090/S1088-4165-07-00320-2
Published electronically:
August 29, 2007
MathSciNet review:
2336607
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce a class of perverse sheaves on a partial flag manifold of a connected reductive group $G$ defined over a finite field which are equivariant for the action of the group of rational points of $G$. The definition of this class is similar to the definition of parabolic character sheaves.
- Robert Bédard, On the Brauer liftings for modular representations, J. Algebra 93 (1985), no. 2, 332–353. MR 786758, DOI https://doi.org/10.1016/0021-8693%2885%2990164-4
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- 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
- George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472
- George Lusztig, Character sheaves. I, Adv. in Math. 56 (1985), no. 3, 193–237. MR 792706, DOI https://doi.org/10.1016/0001-8708%2885%2990034-9
- 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, Homology bases arising from reductive groups over a finite field, Algebraic groups and their representations (Cambridge, 1997) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 517, Kluwer Acad. Publ., Dordrecht, 1998, pp. 53–72. MR 1670764
- George Lusztig, Parabolic character sheaves. I, Mosc. Math. J. 4 (2004), no. 1, 153–179, 311 (English, with English and Russian summaries). MR 2074987, DOI https://doi.org/10.17323/1609-4514-2004-4-1-153-179
- G. Lusztig, Character sheaves on disconnected groups. VI, Represent. Theory 8 (2004), 377–413. MR 2084488, DOI https://doi.org/10.1090/S1088-4165-04-00252-3
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
Received by editor(s):
December 19, 2006
Published electronically:
August 29, 2007
Additional Notes:
The author was supported in part by the National Science Foundation
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.