Erez Lapid
On the Harish-Chandra Schwartz space of $G(F)\backslash G(\mathbb{A})$
Preprint series: ESI preprints

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields

Abstract: We study the Harish-Chandra Schwartz space of an adelic quotient
$G(F)\backslash G(\mathbb{A})$. We state a conjectural spectral
decomposition of it in terms of parabolic induction.
We verify a cuspidal version of this conjecture under additional
hypotheses on the group $G$, which are known to be satisfied for
$G=\operatorname{GL}_n$.


Keywords: Schwartz space, automorphic forms