Sur certains paquets d’Arthur et involution d’Aubert-Schneider-Stuhler généralisée
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- by C. Mœglin
- Represent. Theory 10 (2006), 86-129
- DOI: https://doi.org/10.1090/S1088-4165-06-00270-6
- Published electronically: February 17, 2006
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Abstract:
In this paper, we construct a set of representations for classical $p$-adic groups. This set contains the discrete series and the unipotent representations. It is the basic tool to study Arthur’s packets. The construction is done in two different ways: The first one uses Jacquet modules and gives explicit knowledge. The second one uses a generalization of the Aubert-Schneider-Stuhler involution and gives a resolution in the Grothendieck group.References
- James Arthur, Unipotent automorphic representations: conjectures, Astérisque 171-172 (1989), 13–71. Orbites unipotentes et représentations, II. MR 1021499 arthurnouveau Arthur J.: An introduction to the trace formula, prépublication.
- Anne-Marie Aubert, Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif $p$-adique, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2179–2189 (French, with English summary). MR 1285969, DOI 10.1090/S0002-9947-1995-1285969-0 aubertandco Aubert A.-M., Kutzko P., Morris L.: Algèbres de Hecke des représentations de niveau zéro des groupes réductifs p-adiques. Applications, version très préliminaire communiquée à l’auteur.
- I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. I, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 441–472. MR 579172, DOI 10.24033/asens.1333
- Michael Harris and Richard Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151, Princeton University Press, Princeton, NJ, 2001. With an appendix by Vladimir G. Berkovich. MR 1876802
- Guy Henniart, Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446, DOI 10.1007/s002220050012
- G. Lusztig, Classification of unipotent representations of simple $p$-adic groups. II, Represent. Theory 6 (2002), 243–289. MR 1927955, DOI 10.1090/S1088-4165-02-00173-5
- Colette Moeglin, Points de réductibilité pour les induites de cuspidales, J. Algebra 268 (2003), no. 1, 81–117 (French). MR 2004481, DOI 10.1016/S0021-8693(03)00172-8 unitaire Moeglin C.: Stabilité pour les représentations elliptiques de réduction unipotente: le cas des groupes unitaires, prépublication Février 2003.
- Colette Moeglin, Stabilité en niveau 0, pour les groupes orthogonaux impairs $p$-adiques, Doc. Math. 9 (2004), 527–564 (French, with English summary). MR 2117426
- C. Mœglin, Sur la classification des séries discrètes des groupes classiques $p$-adiques: paramètres de Langlands et exhaustivité, J. Eur. Math. Soc. (JEMS) 4 (2002), no. 2, 143–200 (French, with English summary). MR 1913095, DOI 10.1007/s100970100033
- Colette Mœglin and Marko Tadić, Construction of discrete series for classical $p$-adic groups, J. Amer. Math. Soc. 15 (2002), no. 3, 715–786. MR 1896238, DOI 10.1090/S0894-0347-02-00389-2
- Colette Mœglin, Marie-France Vignéras, and Jean-Loup Waldspurger, Correspondances de Howe sur un corps $p$-adique, Lecture Notes in Mathematics, vol. 1291, Springer-Verlag, Berlin, 1987 (French). MR 1041060, DOI 10.1007/BFb0082712
- Colette Mœglin and Jean-Loup Waldspurger, Paquets stables de représentations tempérées et de réduction unipotente pour $\textrm {SO}(2n+1)$, Invent. Math. 152 (2003), no. 3, 461–623 (French). MR 1988295, DOI 10.1007/s00222-002-0274-3 transfert Moeglin C., Waldspurger J.-L.: Sur le transfert des traces tordues d’un groupe linéaire à un groupe classique p-adique, prépublication, http://www.math.jussieu.fr/~moeglin
- Peter Schneider and Ulrich Stuhler, Representation theory and sheaves on the Bruhat-Tits building, Inst. Hautes Études Sci. Publ. Math. 85 (1997), 97–191. MR 1471867, DOI 10.1007/BF02699536
- Freydoon Shahidi, Local coefficients and normalization of intertwining operators for $\textrm {GL}(n)$, Compositio Math. 48 (1983), no. 3, 271–295. MR 700741
- J.-L. Waldspurger, La formule de Plancherel pour les groupes $p$-adiques (d’après Harish-Chandra), J. Inst. Math. Jussieu 2 (2003), no. 2, 235–333 (French, with French summary). MR 1989693, DOI 10.1017/S1474748003000082
- A. V. Zelevinsky, Induced representations of reductive ${\mathfrak {p}}$-adic groups. II. On irreducible representations of $\textrm {GL}(n)$, Ann. Sci. École Norm. Sup. (4) 13 (1980), no. 2, 165–210. MR 584084, DOI 10.24033/asens.1379
Bibliographic Information
- C. Mœglin
- Affiliation: Institut de Mathématiques de Jussieu, CNRS, 4 place Jussieu, F-75005 Paris
- Email: moeglin@math.jussieu.fr
- Received by editor(s): January 19, 2005
- Received by editor(s) in revised form: December 5, 2005
- Published electronically: February 17, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 10 (2006), 86-129
- MSC (2000): Primary 22E50
- DOI: https://doi.org/10.1090/S1088-4165-06-00270-6
- MathSciNet review: 2209850