|
Representations of reductive groups over finite rings
Author:
G. Lusztig
Translated by:
Journal:
Represent. Theory 8 (2004), 1-14
MSC (2000):
Primary 20G99
Posted:
March 4, 2004
MathSciNet review:
2048585
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper we construct a family of irreducible representations of a Chevalley group over a finite ring  of truncated power series over a field  . This is done by a cohomological method extending that of Deligne and the author in the case  .
- [DL]
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)
- [G]
Paul
Gérardin, Construction de séries discrètes
𝑝-adiques, Lecture Notes in Mathematics, Vol. 462,
Springer-Verlag, Berlin, 1975. Sur les séries discrètes non
ramifiées des groupes réductifs déployés
𝑝-adiques. MR 0396859
(53 #719)
- [L]
G.
Lusztig, Some remarks on the supercuspidal representations of
𝑝-adic semisimple groups, Automorphic forms, representations
and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ.,
Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer.
Math. Soc., Providence, R.I., 1979, pp. 171–175. MR 546595
(81f:22031)
- [S]
Allan
J. Silberger, 𝑃𝐺𝐿₂ over the
𝑝-adics: its representations, spherical functions, and Fourier
analysis, Lecture Notes in Mathematics, Vol. 166, Springer-Verlag,
Berlin, 1970. MR
0285673 (44 #2891)
- [DL]
- P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. Math. 103 (1976), 103-161. MR 52:14076
- [G]
- P. Gérardin, Construction de séries discrètes
 -adiques, Lecture Notes in Math., vol. 462, Springer-Verlag, Berlin, 1975. MR 53:719
- [L]
- G. Lusztig, Some remarks on the supercuspidal representations of
 -adic semisimple groups, Proc. Symp. Pure Math. 33(1) (1979), 171-175, Amer. Math. Soc., Providence, RI. MR 81f:22031
- [S]
- A. Silberger,
 over the  -adics: its representations, spherical functions and Fourier analysis, Lecture Notes in Math., vol. 166 (1970). MR 44:2891
Similar Articles
Retrieve articles in Representation Theory of the American Mathematical Society
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
Email:
gyuri@math.mit.edu
DOI:
http://dx.doi.org/10.1090/S1088-4165-04-00232-8
PII:
S 1088-4165(04)00232-8
Received by editor(s):
August 5, 2002
Received by editor(s) in revised form:
November 21, 2003, and February 4, 2004
Posted:
March 4, 2004
Additional Notes:
Supported in part by the National Science Foundation. Part of this work was done while the author was visiting the Institute for Mathematical Sciences, National University of Singapore, in 2002.
Article copyright:
© Copyright 2004 American Mathematical Society
|
