Algebras and Representation Theory

, Volume 16, Issue 1, pp 275–287 | Cite as

Classification des Représentations Tempérées d’un Groupe p-Adique non Connexe

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Résumé

Soit G le groupe des points définis sur un corps p-adique d’un groupe réductif non connexe. Dans cette note on prouve que toute représentation irréductible tempérée de G est irréductiblement induite d’une essentielle d’un sous-groupe de Lévi cuspidal de G.

Keywords

Groupes p-adiques Représentations Sous-groupes de Levi 

Abstract

Let G be the group of points defined over a p-adic field of a non-connected reductive group. In this note, we prove that every tempered irreducible representation of G is irreducibly induced from an essential one of a cuspidal Levi subgroup of G.

Mathematics Subject Classifications (2010)

11E95 20G05 20G15 

References

  1. 1.
    Arthur, J.: On elliptic tempered characters. Acta Math. 171, 73–138 (1993)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bernstein, J., Zelevinsky, Z.; Induced representations of reductive p-adic groups I. Ann. Sci. Ec. Norm. Super. 4ème Série. 10, 441–472 (1977)MathSciNetMATHGoogle Scholar
  3. 3.
    Casselman, W.: Characters and Jacquet modules. Math. Ann. 230, 101–105 (1977)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Clozel, L.: Invariant analysis on the Schwartz space of a reductive p-adic group. In: Harmonic Analysis on Reductive Groups, Progress in Mathematics, vol. 101, pp. 101–121. Birkhauser, Boston (1991)CrossRefGoogle Scholar
  5. 5.
    Clozel, L.: Orbital integrals on p-adics groups. A proof of the Howe conjecture. Ann. Math. 129, 237–251 (1989)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Deligne, P.: Le support du caractère d’une représentation supercuspidale. C. R. Acad. Sci. Paris Ser A–B 283(4), Aii, A155–A157 (1976)Google Scholar
  7. 7.
    Van Dijk, G.: Computation of certain induced characters of p-adic groups. Math. Ann. 199, 229–240 (1972)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Harish-Chandra: The Plancherel formula for reductive p-adic groups. In: Collected Papers, vol IV, pp. 353–367. Springer, New York (1984)Google Scholar
  9. 9.
    Harish-Chandra: Supertempered distributions on real reductive groups. Studies in applied math. Adv. Math. Supp. Stud. 8, 139–158 (1983)MathSciNetGoogle Scholar
  10. 10.
    Herb, R.: Elliptic representations for Sp(2n) et SO(n). Pac. J. Math. 161, 347–358 (1993)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Herb, R.: Supertempered virtual characters. Compos. Math. 93, 139–154 (1994)MathSciNetMATHGoogle Scholar
  12. 12.
    Kazhdan, D.: Cuspidal geometry of p-adic groups. J. Anal. Math. 47, 1–36 (1986)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Silberger, A.J.: Introduction to harmonic analysis on reductive p-adic groups. In: Mathematical Notes, no. 23. Princeton University Press, Princeton (1979)Google Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Laboratoire de Théorie des Groupes, Représentations—ApplicationsInstitut de Mathématiques de JussieuParisFrance

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