Abstract:In this paper we continue the study of character sheaves on a reductive group. To each subset of the set of simple reflections in the Weyl group we associate an algebra of the same kind as an Iwahori Hecke algebra with unequal parameters in terms of parabolic character sheaves. We also prove a Mackey type formula for character sheaves. We define a duality operation for character sheaves. We also prove a quasi-rationality property for character sheaves.
- Dean Alvis, The duality operation in the character ring of a finite Chevalley group, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 6, 907–911. MR 546315, DOI 10.1090/S0273-0979-1979-14690-1
- 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
- Charles W. Curtis, Truncation and duality in the character ring of a finite group of Lie type, J. Algebra 62 (1980), no. 2, 320–332. MR 563231, DOI 10.1016/0021-8693(80)90185-4
- Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520, DOI 10.1007/BF02684780
- N. Kawanaka, Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field, Invent. Math. 69 (1982), no. 3, 411–435. MR 679766, DOI 10.1007/BF01389363
- George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
- George Lusztig, Character sheaves. I, Adv. in Math. 56 (1985), no. 3, 193–237. MR 792706, DOI 10.1016/0001-8708(85)90034-9
- G. Lusztig, Character sheaves on disconnected groups. I, Represent. Theory 7 (2003), 374–403. MR 2017063, DOI 10.1090/S1088-4165-03-00204-8
- 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 10.17323/1609-4514-2004-4-1-153-179
- G. Lusztig
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Received by editor(s): November 9, 2006
- Received by editor(s) in revised form: January 21, 2006
- Published electronically: August 17, 2006
- Additional Notes: Supported in part by the National Science Foundation.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Represent. Theory 10 (2006), 314-352
- MSC (2000): Primary 20G99
- DOI: https://doi.org/10.1090/S1088-4165-06-00314-1
- MathSciNet review: 2240704