Electronic Only Electronic Research Announcements
Representation Theory
ISSN 1088-4165
     

Remarks on Springer's representations

Author(s): G. Lusztig
Journal: Represent. Theory 13 (2009), 391-400.
MSC (2000): Primary 20G99
Posted: September 3, 2009
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We give an explicit description of a set of irreducible representations of a Weyl group which parametrizes the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre concerning the conjugacy class of a power of a unipotent element in a connected reductive group.


References:

[A]
D. Alvis, Induce/restrict matrices for exceptional Weyl groups, arxiv:RT/0506377.

[HS]
D. Holt and N. Spaltenstein, Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic, J. Austral. Math. Soc. (A) 38 (1985), 330-350. MR 779199 (86g:17007)

[L1]
G. Lusztig, Irreducible representations of finite classical groups, Invent. Math. 43 (1977), 125-175. MR 0463275 (57:3228)

[L2]
G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math. 42 (1981), 169-178. MR 641425 (83c:20059)

[L3]
G. Lusztig, Characters of reductive groups over a finite field, Ann. Math. Studies 107, Princeton Univ. Press, 1984. MR 742472 (86j:20038)

[L4]
G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), 205-272. MR 732546 (86d:20050)

[L5]
G. Lusztig, Unipotent elements in small characteristic, Transform. Groups. 10 (2005), 449-487. MR 2183120 (2006m:20074)

[L6]
G. Lusztig, Unipotent classes and special Weyl group representations, J. Algebra 321 (2009), 3418-3449. MR 2510055

[LS]
G. Lusztig and N. Spaltenstein, On the generalized Springer correspondence for classical groups, Algebraic groups and related topics, Adv. Stud. Pure Math. 6, North-Holland and Kinokuniya, 1985, pp. 289-316. MR 803339 (87g:20072a)

[Se]
J.-P. Serre, Letters to G.Lusztig, Nov. 15, 2006, Nov. 9, 2008.

[S1]
N. Spaltenstein, Classes unipotentes et sousgroupes de Borel, Lecture Notes in Mathematics, vol. 946, Springer-Verlag, 1982. MR 672610 (84a:14024)

[S2]
N. Spaltenstein, Nilpotent classes and sheets in of Lie algebras in bad characteristic, Math. Z. 181 (1982), 31-48. MR 671712 (83m:17007)

[S3]
N. Spaltenstein, Nilpotent classes in Lie algebras of type $ F_{4}$ over fields of characteristic $ 2$, J. Fac. Sci. Univ. Tokyo, IA 30 (1984), 517-524. MR 731515 (85g:20056)

[Sp]
T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173-207. MR 0442103 (56:491)

[X1]
T. Xue, Nilpotent orbits in classical Lie algebras over $ F_{2^{n}}$ and Springer's correspondence, Proc. Nat. Acad. Sci. USA 105 (2008), 1126-1128. MR 2375447 (2009c:14096)

[X2]
T. Xue, Nilpotent orbits in classical Lie algebras over finite fields of characteristic $ 2$ and the Springer correspondence, Represent. Theory 13 (electronic), (2009), 371-390.


Similar Articles:

Retrieve articles in Representation Theory 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

DOI: 10.1090/S1088-4165-09-00358-6
PII: S 1088-4165(09)00358-6
Received by editor(s): May 5, 2009
Posted: September 3, 2009
Additional Notes: Supported in part by the National Science Foundation
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google