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Sur les paquets d’Arthur aux places réelles, translation

  • Colette Moeglin
  • David Renard
Conference paper
Part of the Simons Symposia book series (SISY)

Résumé.

This article is part of a project which aims to describe as explicitly as possible the Arthur packets of classical real groups and to prove a multiplicity one result for them. Let G be a symplectic or special orthogonal real group, and \(\psi : W_{\mathbb R}\times \mathbf {SL}_2(\mathbb C)\rightarrow { }^{LG}\) be an Arthur parameter for G. Let A(ψ) the component group of the centralizer of ψ in \(\widehat G\). Attached to ψ is a finite length unitary representation πA(ψ) of G × A(ψ), which is characterized by the endoscopic identities (ordinary and twisted) it satisfies.

In (Moeglin et Renard, Sur les paquets d’Arthur des groupes classiques réels, arXiv :1703.07226) we gave a description of the irreducible components of πA(ψ) when the parameter ψ is “very regular, with good parity”. In the present paper, we use translation of infinitesimal character to describe πA(ψ) in the general good parity case from the representation πA(ψ+) attached to a very regular, with good parity, parameter ψ+ obtained from ψ by a simple shift.

Mots-clé:

Local components of square integrable Automorphic forms Arthur’s packets Translation and transfer 

Réfèrences

  1. [ABV]
    J. Adams, D. Barbasch et D. Vogan. The Langlands classification and irreducible characters for real reductive groups, volume 104 of Progress in Mathematics. Birkhäuser Boston, Inc., Boston, MA, 1992.CrossRefGoogle Scholar
  2. [AJ]
    J. Adams et J. Johnson. Endoscopic groups and packets of nontempered representations. Compositio Math., 64(3) : 271–309, 1987.MathSciNetzbMATHGoogle Scholar
  3. [AMR]
    N. Arancibia, C. Moeglin et D. Renard. Paquets d’Arthur des groupes classiques et unitaires, cas cohomologique, à para\(\hat {\i }\)tre dans Ann de la factulté des sciences de Toulouse. arXiv :1507.01432.Google Scholar
  4. [Art]
    J. Arthur. The endoscopic classification of representations, volume 61 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, RI, 2013. Orthogonal and symplectic groups.Google Scholar
  5. [BC]
    N. Bergeron et L. Clozel, Comparaison des exposants à lintérieur dun paquet dArthur archimédien. Annales de l’institut Fourier, Tome 63 (2013) no. 1 p. 113-154CrossRefGoogle Scholar
  6. [HS]
    H. Hecht et W. Schmidt. Characters, asymptotics and \(\mathfrak {n}\)-homology of Harish-Chandra modules. Acta Math., 151 : 49–151, 1983.Google Scholar
  7. [KS]
    R. Kottwitz et D. Shelstad. Foundations of twisted endoscopy. Astérisque volume 255, Soc. Math de France, 1999.Google Scholar
  8. [KV]
    A. Knapp et D. Vogan. Cohomological induction and unitary representations, volume 45 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1995.CrossRefGoogle Scholar
  9. [M]
    C. Moeglin. Paquets d’Arthur spéciaux unipotents aux places archimédiennes et correspondance de Howe. Progress in Math. Proceedings of the conference in honnor of R. Howe ; Cogdell J., Kim J., Zhu C. editors.Google Scholar
  10. [MRa]
    C. Moeglin et D. Renard. Paquets d’Arthur des groupes classiques complexes. Contemporary Math. A paraître.Google Scholar
  11. [MRb]
    C. Moeglin et D. Renard. Sur les paquets d’Arthur des groupes classiques réels, à paraître dans JEMS. arXiv :1703.07226Google Scholar
  12. [MRc]
    C. Moeglin et D. Renard. Sur les paquets d’Arthur des groupes non quasi-déployés, \(\grave {\mathrm{a}}\) para\(\hat {\i }\)tre dans Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms : CIRM Jean-Morlet Chair, Spring 2016, Springer Verlag.Google Scholar
  13. [MW]
    C. Moeglin et J. L. Waldspurger. Stabilisation de la formule des traces tordue. Progress in Math, 316 et 317. 2016.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, Institut de Mathématiques de JussieuParisFrance
  2. 2.Centre de Mathématiques Laurent SchwartzEcole PolytechniquePalaiseauFrance

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