Constant term of smooth 𝐻_{𝜓}-spherical functions on a reductive 𝑝-adic group

Delorme, Patrick

doi:10.1090/S0002-9947-09-04925-3

Constant term of smooth $H_\psi$-spherical functions on a reductive $p$-adic group
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Trans. Amer. Math. Soc. 362 (2010), 933-955 Request permission

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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