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La Variante infinitésimale de la formule des traces de Jacquet—Rallis pour les groupesunitaires

Published online by Cambridge University Press:  20 November 2018

Michał Zydor
Affiliation:
Université Paris Diderot, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR7586, Bâtiment Sophie Germain, Case 7012, 75205 PARIS Cedex 13, France courriel: michalz@weizmann.ac.il
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Résumé

Nous établissons une variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes unitaires. Notre formule s’obtient par intégration d'un noyau tronqué á la Arthur. Elle posséde un côté géométrique qui est une somme de distributions ${{J}_{\mathfrak{o}}}$ indexée par les classes d'éléments de l'algébre de Lie de $U\,\left( n\,+\,1 \right)$ stables par $U\left( n \right)$ -conjugaison ainsi qu'un “côté spectral” formé des transformées de Fourier des distributions précédentes. On démontre que les distributions ${{J}_{\mathfrak{o}}}$ sont invariantes et ne dépendent que du choix de la mesure de Haar sur $U\left( n \right)\left( \mathbb{A} \right)$ . Pour des classes $\mathfrak{o}$ semi-simples réguliéres, ${{J}_{\mathfrak{o}}}$ est une intégrale orbitale relative de Jacquet-Rallis. Pour les classes $\mathfrak{o}$ dites relativement semi-simples régulières, on exprime ${{J}_{\mathfrak{o}}}$ en terme des intégrales orbitales relatives régularisées á l'aide des fonctions zêta.

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Research Article
Copyright
Copyright © Canadian Mathematical Society 2016

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