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Formes automorphes de carré intégrable non cuspidales

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Résumé

Le but de cet article est de poser des conjectures permettant de caractériser, parmi les formes automorphes de carré intégrable, celles qui ne sont pas cuspidales, en termes de paramètres d’Arthur. Quelques cas particuliers sont prouvés.

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Références

  1. Adams, J., Barbasch, D., Vogan, D.: The Langlands classification and irreducible characters for real reductive groups. Progress in Math, vol. 104. Birkhäuser (1992)

  2. Adams J., Johnson J.: Endoscopic groups and packets of non-tempered representations. Compos. Math. 64, 271–309 (1987)

    MATH  MathSciNet  Google Scholar 

  3. Arthur, J.: Unipotent automorphic representations: conjectures. In: Orbites Unipotentes et Représentations II, vol. 171–172, pp. 13–72. Astérisque (1989)

  4. Arthur, J.: Unipotent automorphic representations; global motivation. In: Automorphic Forms, Shimura Varieties and L-functions, vol. 1. Clozel, Milne editors, perspectives in Math. vol 10. Academic Press, London (1990)

  5. Arthur J.: An introduction to the trace formula. Clay Math. Proc. 4, 1–253 (2005)

    MathSciNet  Google Scholar 

  6. Arthur, J.: A note on L-packets. Pure and applied math. quarterly, 2 (special issue: in honor of J. H. Coates, part 1 of 2), pp. 199–217 (2006)

  7. Arthur J.: Automorphic representations of GSp(4). In: Hida, H., Ramakr-ishnan, D., Shahidi, F.(eds) Contributions to Automorphic forms, Geometry, and Number Theory (Shalika volume), pp. 65–81. Johns Hopkins University Press, Baltimore (2004)

    Google Scholar 

  8. Bergeron N., Clozel L.: Spectre automorphe des variétés hyperboliques et applications topologiques. Asterisque 303, 214 (2005)

    MathSciNet  Google Scholar 

  9. Bernstein I.N., Zelevinsky A.V.: Induced representations of reductive p-adic groups 1. Ann. l’ENS 10, 147–185 (1977)

    MathSciNet  Google Scholar 

  10. Franke J.: Harmonic analysis on weighted L 2 spaces. Ann. ENS 31, 181–279 (1998)

    MATH  MathSciNet  Google Scholar 

  11. Harris, M., Taylor, R.: The geometry and cohomology of some simple Shimura varieties. Annals of Math Studies, vol. 151. Princeton University Press, New Jersery (2001)

  12. Henniart G.: Une preuve simple des conjectures de Langlands pour GL n sur un corps p-adique. Invent. Math. 139, 439–455 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Jacquet, H., Langlands, R.: Automorphic forms on GL(2), vol. 114. Springer, LN (1970)

  14. Jacquet H., Lapid E., Rogawski J.: Periods of automorphic forms. J. Am. Math. Soc. 12(1), 173–240 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jacquet, H., Shalika, J.: On Euler products and the classification of automorphic representations I, II. Am. J. Math. 103, 499–558, 777–815 (1981)

    Google Scholar 

  16. Johnson J.: Stable base change \({\mathbb{C}/\mathbb{R}}\) of certain derived functor modules. Math. Ann. 287, 467–493 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  17. Labesse J.-P.: Cohomologie, stabilisation et changement de base. Asterisque 257, 160 (1999)

    MathSciNet  Google Scholar 

  18. Langlands, R.: On the functional equations satisfied by Eisenstein series, vol. 544. Springer, LN

  19. Langlands, R.: Euler Products. Yale University Press, New Haven (1967)

    Google Scholar 

  20. Laumon, G.G., Ngo, B.-C.: Le lemme fondamental pour les groupes unitaires. arXiv AG/ 0404454, à paraître Annals of Math

  21. Li, J.-S., Schwermer, J.: On the cuspidal cohomology of arithmetic groups. Am. J. Math. (to appear) (2008)

  22. Mœglin C.: Sur certains paquets d’Arthur et involution d’Aubert–Schneider–Stuhler généralisée. Represent. Theory 10, 86–129 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  23. M0œglin, C.: Classification des séries discrètes pour certains groupes classiques p-adiques. Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory, volume en l’honneur de R. Howe, collectif. Lecture Notes Series, IMS NUS, vol. 12, pp. 152–209 (2007)

  24. Mœglin, C.: Classification et Changement de base pour les séries discrètes des groupes unitaires p-adiques. Pac. J. Math. 233(1), pp.159–204 (2007)

    Google Scholar 

  25. Mœglin, C.: Paquets d’Arthur discrets pour un groupe classique p-adique. À paraître dans le volume en l’honneur de S. Gelbart, publication de l’AMS. http://www.math.jussieu.fr/~moeglin

  26. Mœglin, C.: Paquets d’Arthur pour les groupes classiques; point de vue combinatoire. Mem. AMS. 194(908), 261 pp (2008). arXiv, GR/0610189

  27. Mœglin C.: Classification des séries discrètes: paramètres de Langlands et exhaustivité. JEMS 4, 143–200 (2002)

    Article  MATH  Google Scholar 

  28. Mœglin C., Tadic M.: Construction of discrete series for classical p-adic groups. J. l’AMS 15, 715–786 (2002)

    MATH  Google Scholar 

  29. Mœglin C., Waldspurger J.-L.: Sur le transfert des traces d’un groupe classique p-adique à un groupe linéaire tordu. Sel. Math. 12, 433–516 (2006)

    Article  MATH  Google Scholar 

  30. Mœglin C., Waldspurger J.-L.: Le spectre résiduel de GL(N). Ann. l’ENS 22, 605–674 (1989)

    MATH  Google Scholar 

  31. Mœglin, C., Waldspurger J.-L.: Décomposition spectrale et séries d’Eisenstein; une paraphrase de l’Ecriture, vol. 113. Birkhäuser, PM (1994)

  32. Ngo B.-C.: Fibration de Hitchin et endoscopie. Inventiones 164, 399–453 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  33. Ngo, B.-C.: Le lemme fondamental pour les algèbres de Lie. Prépublication (2007)

  34. Schwermer, J.: The cohomology approach to cuspidal automorphic representations (2008) (in press)

  35. Shahidi F.: A proof of Langlands’ conjecture on Plancherel measures; complementary series for p-adic groups. Ann. Math. 132, 273–330 (1990)

    Article  MathSciNet  Google Scholar 

  36. Shahidi F.: On certain L-functions. Am. J. Math. 103, 297–355 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  37. Soudry D.: On Langlands functoriality from classical groups to GL * n . Asterisque 298, 335–390 (2005)

    MathSciNet  Google Scholar 

  38. Speh B., Vogan D.: Reducibility of generalized principal series representations. Acta Math. 145, 227–299 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  39. Vogan D., Zuckerman G.: Unitary representations with non zero cohomology. Compos. Math. 53, 51–90 (1984)

    MATH  MathSciNet  Google Scholar 

  40. Waldspurger J.-L.: Le groupe GL N tordu sur un corps p-adique, 1e et 2e partie. Duke Math. J. 137, 185–336 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  41. Waldspurger J.-L.: Endoscopie et Changement de caractéristique. JIMJ 5.3, 423–525 (2006)

    Article  MathSciNet  Google Scholar 

  42. Waldspurger, J.-L.: L’endoscopie tordue n’est pas si tordue: intégrales orbitales. prépublication, mai. à paraître aux mémoires de l’AMS (2006)

  43. Zelevinsky A.V.: Induced representations of reductive p-adic groups II. Ann. l’ENS 13, 165–210 (1980)

    MATH  MathSciNet  Google Scholar 

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  1. Institut de mathématiques de Jussieu, 175 rue du Chevaleret, 75013, Paris, France

    C. Mœglin

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Mœglin, C. Formes automorphes de carré intégrable non cuspidales. manuscripta math. 127, 411–467 (2008). https://doi.org/10.1007/s00229-008-0205-8

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