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Representations of reductive groups over finite rings

Author(s): G. Lusztig
Journal: Represent. Theory 8 (2004), 1-14.
MSC (2000): Primary 20G99
Posted: March 4, 2004
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Abstract: In this paper we construct a family of irreducible representations of a Chevalley group over a finite ring $R$ of truncated power series over a field $\mathbf F_q$. This is done by a cohomological method extending that of Deligne and the author in the case $R=\mathbf F_q$.

References:

[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 $p$-adiques, Lecture Notes in Math., vol. 462, Springer-Verlag, Berlin, 1975. MR 53:719

[L]
G. Lusztig, Some remarks on the supercuspidal representations of $p$-adic semisimple groups, Proc. Symp. Pure Math. 33(1) (1979), 171-175, Amer. Math. Soc., Providence, RI. MR 81f:22031

[S]
A. Silberger, $PGL_{2}$ over the $p$-adics: its representations, spherical functions and Fourier analysis, Lecture Notes in Math., vol. 166 (1970). MR 44:2891

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Additional Information:

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: gyuri@math.mit.edu

DOI: 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.
Copyright of article: Copyright 2004, American Mathematical Society

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