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Unramified representations of reductive groups over finite rings
Author(s):
Alexander
Stasinski
Journal:
Represent. Theory
13
(2009),
636-656.
MSC (2000):
Primary 20G99;
Secondary 14L15
Posted:
November 9, 2009
MathSciNet review:
2558788
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Additional information
Abstract:
Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic  , extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig's results to reductive groups over arbitrary finite local rings. This generalization uses the Greenberg functor and the theory of group schemes over Artinian local rings.
References:
-
- 1.
- R. W. Carter, Finite Groups of Lie Type, John Wiley & Sons Inc., New York, 1985. MR 794307 (87d:20060)
- 2.
- P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103-161. MR 0393266 (52:14076)
- 3.
- M. Demazure, Schémas en groupes réductifs, Bull. Soc. Math. France 93 (1965), 369-413. MR 0197467 (33:5632)
- 4.
- F. Digne and J. Michel, Representations of Finite Groups of Lie Type, Cambridge University Press, Cambridge, 1991. MR 1118841 (92g:20063)
- 5.
- P. Gérardin, Construction de séries discrètes
 -adiques, Lecture Notes in Mathematics 462, Springer-Verlag, Berlin, 1975. MR 0396859 (53:719) - 6.
- M. J. Greenberg, Schemata over local rings, Ann. of Math. (2) 73 (1961), 624-648. MR 0126449 (23:A3745)
- 7.
- M. J. Greenberg, Schemata over local rings. II, Ann. of Math. (2) 78 (1963), 256-266. MR 0156855 (28:98)
- 8.
- G. Hill, Regular elements and regular characters of
 , J. Algebra 174 (1995), no. 2, 610-635. MR 1334228 (96i:20055) - 9.
- G. Hill, Semisimple and cuspidal characters of
 , Comm. Algebra 23 (1995), no. 1, 7-25. MR 1311772 (96c:22030) - 10.
- J. C. Jantzen, Representations of Algebraic Groups, volume 107 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2003. MR 2015057 (2004h:20061)
- 11.
- G. Lusztig, Representations of Finite Chevalley Groups, American Mathematical Society, Providence, R.I., 1978. MR 518617 (80f:20045)
- 12.
- G. Lusztig, Representations of reductive groups over finite rings, Represent. Theory 8 (2004), 1-14. MR 2048585 (2005d:20077)
- 13.
- SGA 3, Schémas en groupes, I-III, dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics 151-153, Springer-Verlag, Berlin, 1970. MR 0274458 (43:223a)
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Additional Information:
Alexander
Stasinski
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
Address at time of publication:
School of Mathematics, University of Southampton, Southampton, SO17 1BJ United Kingdom
Email:
a.stasinski@soton.ac.uk
DOI:
10.1090/S1088-4165-09-00350-1
PII:
S 1088-4165(09)00350-1
Received by editor(s):
September 16, 2008
Received by editor(s) in revised form:
February 17, 2009
Posted:
November 9, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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