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Espace des coefficients de représentations admissibles d’un groupe réductif p-adique

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Noncommutative Harmonic Analysis

Part of the book series: Progress in Mathematics ((PM,volume 220))

Résumé

Soit G le groupe des points sur F d’un groupe linéaire algébrique réductif et connexe défini sur F, où F est un corps local non archimédien de caractéristique nulle. On note A G le plus grand tore déployé du centre de G.

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Références

  1. J. Arthur, Intertwining operators and residues I. Weighted characters, J. Funct Anal. 84 (1989), 19–84.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Bernstein, Representations of p-adic groups. Lectures given at Harvard University, Fall 1992, Notes by K. E. Rummelhart.

    Google Scholar 

  3. J. Bernstein, P. Deligne, Le centre de Bernstein, rédigé par P. Deligne. Travaux en cours. Representations of reductive groups over a local field. 1–32. Hermann, Paris, 1984.

    Google Scholar 

  4. J. Bernstein, A. Zelevinsky, Induced representations of reductive p-adic groups. I, Ann. E.N.S. 10 (1977), 441–472.

    MATH  Google Scholar 

  5. N. Bourbaki, Eléments de Mathématiques, Algèbre Commutative, Chapitre 5 et 6, Actualités scientifique set industrielles 1308, Hermann, Paris.

    Google Scholar 

  6. C.J. Bushnell, Representations of reductive p-adic groups: localization of Hecke agebras and applications. J. London Math. Soc. 63 (2001), 364–386.

    Article  MathSciNet  MATH  Google Scholar 

  7. C.J. Bushnell, P.C. Kutzko, Smooth representations of reductive p-adic groups: structure theory via types. Proc. London Math. Soc. 77 (1998), 582–634.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Carmona, Sur la classification des modules admissible irréductibles, Non commutative harmonic analysis and Lie groups (Marseille, 1982), 11–34, Lecture Notes in Math., 1020, Springer, Berlin 1983.

    Google Scholar 

  9. W. Casselman, Introduction to thetheory of admissible representations of reductive p-adic groups, preprint, 1993.

    Google Scholar 

  10. W. Casselman, D. Milicic, Asymptotic behavior of coefficients of admissible representations, Duke Math. J. 49 (1982), 869–930.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Delorme, avec un appendice de M. Tinfou, Espace de Schwartz pour la transformation de Fourier hypergéometriqué, Jour. Funct. Anal. 168, (1999), 239–312.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Franke, Harmonic analysis in weighted L 2-spaces, Ann. Sci. Ecole Norm. Sup. 31 (1988), 181–279.

    MathSciNet  Google Scholar 

  13. Harish-Chandra, Spherical functions on a semisimple Lie group I, Amer. J. of Math., 80 (1958), 241–310.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Hecht, W. Schmid, Characters, asymptotic and n-homology of Harish-Chandra modules, Acta Math. 151 (1983), 50–151.

    Article  MathSciNet  Google Scholar 

  15. R.P. Langlands, On the classification of irreducible representations of real algebraic groups, in Representation theory and harmonic analysis on semisimple Lie groups Mathematical Surveys and Monographs 31, edited by P. Sally and D. Vogan Jr, 1988, A.M.S., Providence, 101–170.

    Google Scholar 

  16. L. Schwartz, Théorie des distributions, Hermann, Paris 1966.

    MATH  Google Scholar 

  17. A.S. Silberger, Introduction to harmonic analysis on reductive p-adic groups. Mathematical Notes 23, Princeton University Press, Princeton, 1979.

    Google Scholar 

  18. S. Souaifi, Fonctions K et D (G / H)-finies sur un espace symétrique réductif, J. Funct. Anal. 195 (2002), 371–443.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Tits, Reductive groups over local field, in Automorphic forms, representations and L-functions, Proceedings of Symposia in Pure Mathematics 33-Part I (ed. A. Borel and W. Casselman), A.M.S., Providence, RI 1979, 29–69.

    Google Scholar 

  20. J.L. Waldspurger, Cohomologie des espaces de forms automorphes, Séminaire Bourbaki, Vol. 1995/96. Astérisque 241 (1997), Exp. 809, 139–156.

    MathSciNet  Google Scholar 

  21. J.L. Waldspurger, La formule de Plancherel pour les groups réductifs p-adiques, d’après Harish-Chandra, prépublication.

    Google Scholar 

  22. G. Warner, Harmonic analysis on semi-simple Lie groups I, Grundlehren der math. Wissen. In Einz., 188, Springer Verlag, Berlin, Heidelberg. NewYork, 1972.

    Google Scholar 

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Delorme, P. (2004). Espace des coefficients de représentations admissibles d’un groupe réductif p-adique. In: Delorme, P., Vergne, M. (eds) Noncommutative Harmonic Analysis. Progress in Mathematics, vol 220. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8204-0_6

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  • DOI: https://doi.org/10.1007/978-0-8176-8204-0_6

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6489-7

  • Online ISBN: 978-0-8176-8204-0

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