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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Geometric side of a local relative trace formula


Authors: P. Delorme, P. Harinck and S. Souaifi
Journal: Trans. Amer. Math. Soc. 371 (2019), 1815-1857
MSC (2010): Primary 11F72, 22E50
DOI: https://doi.org/10.1090/tran/7360
Published electronically: October 26, 2018
MathSciNet review: 3894036
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Abstract: Following a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive $ p$-adic group $ G$ relative to a symmetric subgroup $ H= \underline {H}(\textup {F})$ where $ \underline {H}$ is split over the local field $ \textup {F}$ of characteristic zero and $ G = \underline {G} (\textup {F})$ is the restriction of scalars of $ \underline {H} _{\slash \, \textup {E}}$ relative to a quadratic unramified extension $ \textup {E}$ of $ \textup {F}$. We adapt techniques of the proof of the local trace formula by J. Arthur in order to get a geometric expansion of the integral over $ H \times H$ of a truncated kernel associated to the regular representation of $ G$.


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Additional Information

P. Delorme
Affiliation: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, 13453 Marseille, France
Email: patrick.delorme@univ-amu.fr

P. Harinck
Affiliation: CMLS, École Polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau Cedex, France
Email: pascale.harinck@polytechnique.edu

S. Souaifi
Affiliation: Université de Strasbourg, IRMA CNRS, UMR 7501, 7 rue René Descartes, 67084 Strasbourg Cédex, France
Email: sofiane.souaifi@math.unistra.fr

DOI: https://doi.org/10.1090/tran/7360
Keywords: $p$-adic reductive groups, symmetric spaces, local relative trace formula, truncated kernel, orbital integrals
Received by editor(s): September 8, 2015
Received by editor(s) in revised form: September 20, 2016, and July 7, 2017
Published electronically: October 26, 2018
Additional Notes: The first author was supported by a grant of Agence Nationale de la Recherche with reference ANR-13-BS01-0012 FERPLAY
Article copyright: © Copyright 2018 American Mathematical Society