Representations of reductive groups over finite rings
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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
- 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
Additional Information
- G. Lusztig
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@math.mit.edu
- 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: https://doi.org/10.1090/S1088-4165-04-00232-8
- MathSciNet review: 2048585