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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Constant term of smooth $ H_\psi$-spherical functions on a reductive $ p$-adic group


Author: Patrick Delorme
Journal: Trans. Amer. Math. Soc. 362 (2010), 933-955
MSC (2000): Primary 22E50
Published electronically: September 17, 2009
MathSciNet review: 2551511
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Abstract: Let $ \psi$ be a smooth character of a closed subgroup, $ H$, of a reductive $ p$-adic group $ G$. If $ P$ is a parabolic subgroup of $ G$ such that $ PH$ is open in $ G$, we define the constant term of every smooth function on $ G$ which transforms by $ \psi$ under the right action of $ G$. The example of mixed models is given: it includes symmetric spaces and Whittaker models. In this case a notion of cuspidal function is defined and studied. It leads to finiteness theorems.


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Additional Information

Patrick Delorme
Affiliation: Institut de Mathématiques de Luminy, UMR 6206 CNRS, Université de la Méditerranée, 163 Avenue de Luminy, 13288 Marseille Cedex 09, France
Email: delorme@iml.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04925-3
PII: S 0002-9947(09)04925-3
Keywords: Reductive group, non-Archimedean local field, symmetric space, Whittaker model
Received by editor(s): January 1, 2011
Received by editor(s) in revised form: January 1, 2008
Published electronically: September 17, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.