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Character sheaves on disconnected groups, VIII
Author:
G. Lusztig
Journal:
Represent. Theory 10 (2006), 314-352
MSC (2000):
Primary 20G99
Posted:
August 17, 2006
MathSciNet review:
2240704
Full-text PDF Free Access
Abstract |
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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
- [Al]
D. Alvis, The duality operation in the character ring of a finite Chevalley group, Bull. Amer. Math. Soc. 1 (1979), 907-911. MR 0546315 (81e:20012)
- [BBD]
A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, Astérisque 100 (1982). MR 0751966 (86g:32015)
- [Cu]
C.W. Curtis, Truncation and duality in the character ring of a finite group of Lie type, J. Algebra 62 (1980), 320-332. MR 0563231 (81e:20011)
- [De]
P. Deligne, La conjecture de Weil, II, Publ. Math. I.H.E.S. 52 (1980), 137-252. MR 0601520 (83c:14017)
- [Ka]
N. Kawanaka, Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field, Invent. Math. 69 (1982), 411-435. MR 0679766 (84c:20053)
- [L14]
G. Lusztig, Characters of reductive groups over a finite field, Ann. Math. Studies 107, Princeton Univ. Press, 1984. MR 0742472 (86j:20038)
- [L3]
G. Lusztig, Character sheaves, I, Adv. Math. 56 (1985), 193-237; II, vol. 57, 1985, pp. 226-265; III, vol. 57, 1985, pp. 266-315; IV, vol. 59, 1986, pp. 1-63; V, vol. 61, 1986, pp. 103-155. MR 0792706 (87b:20055); MR 0806210 (87m:20118a); MR 0825086 (87m:20118b); MR 0849848 (87m:20118c)
- [L9]
G. Lusztig, Character sheaves on disconnected groups, I, Represent. Theory (electronic) 7 (2003), 374-403; II, vol. 8, 2004, pp. 72-124; III, vol. 8, 2004, pp. 125-144; IV, vol. 8, 2004, pp. 145-178; Errata , vol. 8, 2004, pp. 179-179; V, vol. 8, 2004, pp. 346-376; VI, vol. 8, 2004, pp. 377-413; VII, vol. 9, 2005, pp. 209-266. MR 2017063 (2006d:20090a); MR 2048588 (2006d:20090b); MR 2048589 (2006d:20090c); MR 2048590 (2006d:20090d); MR 2058725; MR 2077486 (2005h:20111); MR 2084488 (2005h:20112); MR 2133758 (2006e:20089)
- [L10]
G. Lusztig, Parabolic character sheaves, I, Moscow Math. J. 4 (2004), 153-179. MR 2074987 (2006d:20091a)
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Additional Information
G. Lusztig
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
DOI:
http://dx.doi.org/10.1090/S1088-4165-06-00314-1
PII:
S 1088-4165(06)00314-1
Received by editor(s):
November 9, 2006
Received by editor(s) in revised form:
January 21, 2006
Posted:
August 17, 2006
Additional Notes:
Supported in part by the National Science Foundation.
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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