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Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires

Part of: Linear algebraic groups and related topics Lie groups

Published online by Cambridge University Press:  18 February 2015

R. Beuzart-Plessis
R. Beuzart-Plessis*
Affiliation:
Institute for Advanced Study, 1 Einstein Drive 08540, Princeton, NJ, USA email rbeuzart@gmail.com
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Abstract

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Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan–Gross–Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.

Keywords

Gan–Gross–Prasad conjectureunitary groupsendoscopy

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields 20G05: Representation theory
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 7 , July 2015 , pp. 1309 - 1371
Copyright
© The Author 2015 

References

Arthur, J., The endoscopic classification of representations: orthogonal and symplectic groups, Colloquium Publication Series, vol. 61 (American Mathematical Society, Providence, RI, 2013).Google Scholar
Aizenbud, A., Gourevitch, D., Rallis, S. and Schiffmann, G., Multiplicity one theorems, Ann. of Math. (2) 172 (2010), 1407–1434.CrossRefGoogle Scholar
Beuzart-Plessis, R., La conjecture locale de Gross-Prasad pour les représentations tempérées de groupes unitaires. Preprint (2012), arXiv:1205.2987 [math.RT].Google Scholar
Beuzart-Plessis, R., Expression d’un facteur epsilon de paire par une formule intégrale, Canad. J. Math. 66 (2014), 993–1049.CrossRefGoogle Scholar
Clozel, L., Characters of nonconnected, reductive p-adic groups, Canad. J. Math. 39 (1987), 149–167.CrossRefGoogle Scholar
Gan, W. T., Gross, B. and Prasad, D., Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups, Astérisque 346 (2012).Google Scholar
Harish-Chandra, Admissible invariant distributions on reductive p-adic groups, University Lecture Series, vol. 16, eds DeBacker, S. and Sally, P. (American Mathematical Society, Providence, RI, 1999).Google Scholar
Jacquet, H., Piatetskii-Shapiro, I. I. and Shalika, J., Rankin–Selberg convolutions, Amer. J. Math. 105 (1983), 367–464.CrossRefGoogle Scholar
Konno, T., Twisted endoscopy and the generic packet conjecture, Israel J. Math. 129 (2002), 253–289.CrossRefGoogle Scholar
Kottwitz, R. and Shelstad, D., Foundations of twisted endoscopy, Astérisque 255 (1999).Google Scholar
Langlands, R. and Shelstad, D., On the definition of transfer factors, Math. Ann. 278 (1987), 219–271.CrossRefGoogle Scholar
Mok, C.-P., Endoscopic classification of representations of quasi-split unitary groups, Mem. Amer. Math. Soc. 235 (2014), no. 1108, doi:10.1090/memo/1108.Google Scholar
Rodier, F., Modèle de Whittaker et caractères de représentations, in Non commutative harmonic analysis, Lecture Notes in Mathematics, vol. 466, eds Carmona, J., Dixmier, J. and Vergne, M. (Springer, 1975), 151–171.CrossRefGoogle Scholar
Shelsta, D., A formula for regular unipotent germs, in Orbites unipotentes et représentations, II, Astérisque, 171–172 (1989), 275–277.Google Scholar
Waldspurger, J.-L., Le lemme fondamental implique le transfert, Compositio Math. 105 (1997), 153–236.CrossRefGoogle Scholar
Waldspurger, J.-L., Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque 269 (2001).Google Scholar
Waldspurger, J.-L., Les facteurs de transfert pour les groupes classiques: un formulaire, Manuscripta Math. 133 (2010), 41–82.CrossRefGoogle Scholar
Waldspurger, J.-L., La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux, Asterique 347 (2012), 103–165.Google Scholar