Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-zdfhw Total loading time: 0.799 Render date: 2022-08-19T06:31:48.459Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Article contents

Le transfert singulier pour la formule des traces de Jacquet–Rallis

Published online by Cambridge University Press:  16 March 2021

Pierre-Henri Chaudouard
Affiliation:
Université de Paris et Sorbonne Université, CNRS, IMJ-PRG, F-75006Paris, Francepierre-henri.chaudouard@imj-prg.fr
Michał Zydor
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI48109, USAzydor@umich.edu

Résumé

La formule des traces relative de Jacquet–Rallis (pour les groupes unitaires ou les groupes linéaires généraux) est une identité entre des périodes des représentations automorphes et des distributions géométriques. Selon Jacquet et Rallis, une comparaison de ces deux formules des traces relatives devrait aboutir à une démonstration des conjectures de Gan–Gross–Prasad et Ichino–Ikeda pour les groupes unitaires. Les termes géométriques des groupes unitaires ou des groupes linéaires sont indexés par les points rationnels d'un espace quotient commun. Nous établissons que ces termes géométriques peuvent être vus comme des fonctionnelles sur des espaces d'intégrales orbitales semi-simples régulières locales. En outre, nous montrons que point par point ces distributions sont en fait égales, via l'identification des espaces d'intégrales orbitales locales donnée par le transfert et le lemme fondamental (essentiellement connus dans cette situation). Cela donne leur comparaison et cela clôt la partie géométrique du programme de Jacquet–Rallis. Notre résultat principal est donc un analogue de la stabilisation de la partie géométrique de la formule des traces due à Langlands, Kottwitz et Arthur.

Abstract

Abstract

The relative trace formula of Jacquet–Rallis (for unitary groups or general linear groups) is an identity between periods of automorphic representations and geometric distributions. According to Jacquet and Rallis a comparison between these two trace formulae should give a proof of the Gan–Gross–Prasad and Ichino–Ikeda conjectures for unitary groups. The geometric terms are parametrized by the rational points of a common quotient space. In this paper, we show that the geometric terms both for unitary groups and general linear groups can be factorized as functionals on the space of local regular semi-simple orbital integrals. Moreover, we show for each rational point of the quotient that the corresponding terms are equal through the identification of the space of local orbital integrals given by the transfer and the fundamental lemma (essentially known in our situation). This gives the full comparison of the geometric sides and this achieves the geometric part of the Jacquet–Rallis program. Our main result is an analog of the geometric stabilization of the Arthur–Selberg trace formula due to Langlands, Kottwitz and Arthur.

Type
Research Article
Copyright
© The Author(s) 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
1
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Le transfert singulier pour la formule des traces de Jacquet–Rallis
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Le transfert singulier pour la formule des traces de Jacquet–Rallis
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Le transfert singulier pour la formule des traces de Jacquet–Rallis
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *