Character sheaves on disconnected groups, VIII

Lusztig, G.

doi:10.1090/S1088-4165-06-00314-1

Character sheaves on disconnected groups, VIII
HTML articles powered by AMS MathViewer

by G. Lusztig

Represent. Theory 10 (2006), 314-352

DOI: https://doi.org/10.1090/S1088-4165-06-00314-1

Published electronically: August 17, 2006

PDF | Request permission

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.

References

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