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Classification des représentations tempérées d'un groupe p-adique

Published online by Cambridge University Press:  20 November 2018

Karem Bettaïeb
Karem Bettaïeb*
Affiliation:
Laboratoire de Théorie des Groupes, Représentations – Applications, Institut de Mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
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Résumé

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Soit $G$ le groupe des points définis sur un corps $p$-adique d'un groupe réductif connexe. A l'aide des caractères virtuels supertempérés de $G$, on prouve (conjectures de Clozel) que toute représentation irréductible tempérée de $G$ est irréductiblement induite d'une essentielle d'un sousgroupe de Lévi de $G$.

Keywords

22E
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 6 , 01 December 2003 , pp. 1121 - 1133
Copyright
Copyright © Canadian Mathematical Society 2003

References

Références

[1] Arthur, J., On Elliptic Tempered Characters. Acta Math. 171(1993), 73–138.Google Scholar
[2] Bernstein, J. et Zelevinsky, Z., Induced representations of reductive p-adic groups I. Ann. Sci. École Norm. Sup. (4) 10(1977), 4–1–472.Google Scholar
[3] Casselman, W., Characters and Jacquet modules. Math. Ann. 230(1977), 1–1–105.Google Scholar
[4] Clozel, L., Invariant harmonic analysis on the Schwartz space of a reductive p-adic group. In: Harmonic Analysis on Reductive Groups, Progr. Math. 101(1991), 1–1–121.Google Scholar
[5] Clozel, L., Orbital integrals on p-adic groups. A proof of the Howe conjecture. Ann. of Math. 129(1989), 237–251.Google Scholar
[6] Deligne, P., Le support du caractère d'une représentation supercuspidale. C. R. Acad. Sci. Paris Sér. A.B (4) 283(1976), Aii, A155–157.Google Scholar
[7] Van Dijk, G., Computation of certain induced characters of p-adic groups. Math. Ann. 199(1972), 229–240.Google Scholar
[8] Harish-Chandra, , The Plancherel Formula for Reductive p-adic Groups. In: Collected Papers, Vol. IV, Springer Verlag, 1984, 353–367.Google Scholar
[9] Harish-Chandra, , Supertempered distributions on real reductive groups. In: Studies in Applied Math., Adv. Math. Suppl. Stud. 8(1983), 139–158.Google Scholar
[10] Herb, R., Elliptic representations for Sp(2n) et SO(n) . Pacific J. Math. 161(1993), 347–358.Google Scholar
[11] Herb, R., Supertempered virtual characters. Compositio Math. 93(1994), 139–154.Google Scholar
[12] Kazhdan, D., Cuspidal Geometry of p-adic Groups. J. Analyse Math. 47(1986), 1–36.Google Scholar
[13] Silberger, A. J., Introduction to harmonic analysis on reductive p-adic groups. Math. Notes 23, Princeton University Press, Princeton, N.J., 1979.Google Scholar