Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-27T19:51:58.813Z Has data issue: false hasContentIssue false

Holomorphie des opérateurs d’entrelacement normalisés à l’aide des paramètres d’Arthur

Published online by Cambridge University Press:  20 November 2018

C. Mœglin*
Affiliation:
CNRS, Institut de Mathématiques de Jussieu, Franc
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we prove holomorphy for certain intertwining operators arising from the theory of Eisenstein series. To do that we need to normalize using the Langlands–Shahidi's normalization arising from the twisted endoscopy and the associated representations of the general linear group.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2010

References

Références

[1] Arthur, J., Unipotent automorphic representations, conjectures. In: Orbites unipotentes et représentations II, Astérisque 171–172(1989), 13–72.Google Scholar
[2] Arthur, J., On local character relations. Selecta Math. 2(1996), 501–579. doi:10.1007/BF02433450Google Scholar
[3] Arthur, J., An introduction to the trace formula. Clay Math. Proc. 4(2005), 1–253.Google Scholar
[4] Arthur, J., A note on L-packets. Pure Appl. Math. Quart. (special issue: in honor of Coates, J. H., part 1 of 2), 2(2006), 199–217.Google Scholar
[5] Arthur, J., A note on L-packets. Pure Appl. Math. Quart. (special issue: in honor of Coates, J. H., A note on L-packets. Pure Appl. Math. Quart. (special issue: in honor of Coates, J. H., Automorphic Representations of GSp(4). In: Contributions to Automorphic Forms, Geometry, and Number Theory (Shalika volume, eds. Hida, H., Ramakrishnan, D., and Shahidi, F.), Johns Hopkins Univ. Press, Baltimore, MD, 2004, 65–81.Google Scholar
[6] Arthur, J., A note on L-packets. Pure Appl. Math. Quart. (special issue: in honor of Coates, J. H., Automorphic Representations of Classical Groups. En préparation.Google Scholar
[7] Aubert, A.-M., Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Transl. Amer. Math. Soc. 347(1995), 2179–2189; avec l’erratum publié dans Transl. Amer. Math. Soc. 348(1996), 4687–4690.Google Scholar
[8] Bernstein et, I. N. Zelevinsky, A. V., Induced Representations of Reductive p-adic groups. I. Ann. Sci. Ecole Norm. Sup. 10(1977), 147–185.Google Scholar
[9] Goldberg, D., Some results on reducibility for unitary groups and local Asai L-functions. Crelle J. 448(1994), 65–95.Google Scholar
[10] Harris et, M. Taylor, R., The geometry and cohomology of some simple Shimura varieties. Ann. of Math Stud. 151, Princeton Univ. Press, 2001.Google Scholar
[11] Henniart, G., Une preuve simple des conjectures de Langlands pour GLn sur un corps p-adique. Invent. Math. 139(2000), 439–455. doi:10.1007/s002220050012Google Scholar
[12] Ginzburg, D., Jiang, D. et Soudry, D., Poles of L-functions and theta lifting for orthogonal groups. Prépublication, 2007.Google Scholar
[13] Kim, H., On local L-function and normalized intertwining operators. Canad. J. Math. 57(2005), 535–597.Google Scholar
[14] Moeglin, C., Sur la classification des séries discrètes des groupes classiques p-adiques; paramètre de Langlands et exhaustivité. J. Eur. Math. Soc. 4(2002), 143–200. doi:10.1007/s100970100033Google Scholar
[15] Moeglin, C., Sur certains paquets d’Arthur et involution d’Aubert–Schneider–Stuhler généralisée. Represent. Theory 10(2006), 86–129. doi:10.1090/S1088-4165-06-00270-6Google Scholar
[16] Moeglin, C., Paquets d’Arthur discrets pour un groupe classique p-adique. Prépublication, 2004; á parâıtre dans le volume en l’honneur de S. Gelbart, Amer. Math. Soc.Google Scholar
[17] Moeglin, C., Paquets d’Arthur discrets pour un groupe classique p-adique. Prépublication, 2004; á parâıtre dans le volume en l’honneur de S. Gelbart, Paquets d’Arthur pour les groupes classiques p-adiques; point de vue combinatoire. Prépublication, 2006.Google Scholar
[18] Moeglin, C., Paquets d’Arthur discrets pour un groupe classique p-adique. Prépublication, 2004; á parâıtre dans le volume en l’honneur de S. Gelbart, Formes automorphes de carré intégrable non cuspidales. Prépublication, 2007; á parâıtre Manuscripta.Google Scholar
[19] Moeglin, C., Paquets d’Arthur discrets pour un groupe classique p-adique. Prépublication, 2004; á parâıtre dans le volume en l’honneur de S. Gelbart, Multiplicité 1 dans les paquets d’Arthur aux places p-adiques. Prépublication, 2007; á parâıtre volume en l’honneur de F. Shahidi.Google Scholar
[20] Moeglin et, C. Tadic, M., Construction of discrete series for classical p-adic groups. J. Amer. Math. Soc. 15(2002), 715–786. doi:10.1090/S0894-0347-02-00389-2Google Scholar
[21] Moeglin et, C. Waldspurger, J.-L., Le spectre résiduel de GL(n). Ann. Sci. Ecole Norm. Sup. 22(1989), 605–674.Google Scholar
[22] Moeglin et, C. Waldspurger, J.-L., Sur le transfert des traces tordues d’un groupe linéaire á un groupe classique p-adique. Selecta Math. 12(2006), 433–516.Google Scholar
[23] Shahidi, F., Local coefficients and intertwining operators for GL(n). Compositio Math. 48(1983), 271–295.Google Scholar
[24] Shahidi, F., On the Ramanujan conjecture and finiteness of poles for certain L-functions. Ann. of Math. 127(1988), 547–584. doi:10.2307/2007005Google Scholar
[25] Shahidi, F., A proof of Langlands’ conjecture on Plancherel measures; complementary series for p-adic groups. Ann. of Math. 132(1990), 273–330. doi:10.2307/1971524Google Scholar
[26] Schneider et, M. Stuhler, U., Representation theory and sheaves on the Bruhat–Tits building. Inst. Hautes Etudes Sci. Publ. Math. 85(1997), 97–191.Google Scholar
[27] Silberger, A., Special representations of reductive p-adic groups are not integrable. Ann. of Math. 111(1980), 571–587. doi:10.2307/1971110Google Scholar
[28] Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques, d’après Harish-Chandra. J. Inst. Math. Jussieu 2(2003), 235–333. doi:10.1017/S1474748003000082Google Scholar
[29] Zelevinsky, A. V., Induced Representations of Reductive p-adic groups II. Ann. Sci. Ecole Norm. Sup. 13(1980), 165–210.Google Scholar