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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Representations of reductive groups over finite rings
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by G. Lusztig
Represent. Theory 8 (2004), 1-14
Published electronically: March 4, 2004


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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Bibliographic 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