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Representation Theory
Representation Theory
ISSN 1088-4165


Representations of reductive groups over finite rings

Author: G. Lusztig
Translated by:
Journal: Represent. Theory 8 (2004), 1-14
MSC (2000): Primary 20G99
Published electronically: March 4, 2004
MathSciNet review: 2048585
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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 $R$ 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 [Enhancements On Off] (What's this?)

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  • [G] Paul Gérardin, Construction de séries discrètes 𝑝-adiques, Lecture Notes in Mathematics, Vol. 462, Springer-Verlag, Berlin-New York, 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) 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-New York, 1970. MR 0285673 (44 #2891)

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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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
Published electronically: 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

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