Nous établissons une généralisation de la dualité de Casselman aux espaces symétriques réductifs p-adiques et nous étudions le comportement asymptotique de certains coefficients. Nous prouvons aussi un anologue d'un lemme de Langlands grâce auquel nous obtenons un résultat de disjonction de certaines parties de la décomposition de Cartan de l'espace symétrique.
We establish a generalization of Casselman's pairing to p-adic reductive symmetric spaces and we study the asymptotic behaviour of certain coefficients. Also an analogous of a Langlands lemma is proved and used to get a disjonction result for the Cartan decomposition of the symmetric space.
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@article{CRMATH_2007__344_7_421_0,
author = {Nathalie Lagier},
title = {Asymptotiques de fonctions sur un espace sym\'etrique r\'eductif \protect\emph{p}-adique},
journal = {Comptes Rendus. Math\'ematique},
pages = {421--424},
publisher = {Elsevier},
volume = {344},
number = {7},
year = {2007},
doi = {10.1016/j.crma.2007.02.002},
language = {fr},
}
Nathalie Lagier. Asymptotiques de fonctions sur un espace symétrique réductif p-adique. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 421-424. doi : 10.1016/j.crma.2007.02.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.02.002/
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