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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Representations of reductive groups over finite rings
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by G. Lusztig PDF
Represent. Theory 8 (2004), 1-14 Request permission


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 $R=\mathbf F_q$.
  • P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161. MR 393266, DOI 10.2307/1971021
  • 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, DOI 10.1007/BFb0082161
  • 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, DOI 10.1090/pspum/033.1/546595
  • Allan J. Silberger, $\textrm {PGL}_{2}$ 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, DOI 10.1007/BFb0059369
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Additional Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Email:
  • 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.
  • © Copyright 2004 American Mathematical Society
  • Journal: Represent. Theory 8 (2004), 1-14
  • MSC (2000): Primary 20G99
  • DOI:
  • MathSciNet review: 2048585