Constant term of smooth $H_\psi$-spherical functions on a reductive $p$-adic group
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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.References
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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
- Received by editor(s): January 1, 1100
- Received by editor(s) in revised form: January 1, 2008
- Published electronically: September 17, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 933-955
- MSC (2000): Primary 22E50
- DOI: https://doi.org/10.1090/S0002-9947-09-04925-3
- MathSciNet review: 2551511