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Globalization of Distinguished Supercuspidal Representations of $\GL(n)$ |
Canad. Math. Bull. 45(2002), 220-230
Published:2002-06-01
Printed: Jun 2002
Printed: Jun 2002
- Jeffrey Hakim
- Fiona Murnaghan
Abstract
An irreducible supercuspidal representation $\pi$ of $G=
\GL(n,F)$, where $F$ is a nonarchimedean local field of
characteristic zero, is said to be ``distinguished'' by a
subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if
$\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue
of this notion for and irreducible, automorphic, cuspidal
representation associated to $\GL(n)$. Under certain general
hypotheses, it is shown in this paper that every distinguished,
irreducible, supercuspidal representation may be realized as a
local component of a distinguished, irreducible automorphic,
cuspidal representation. Applications to the theory of
distinguished supercuspidal representations are provided.
| MSC Classifications: |
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 22E35 - Analysis on $p$-adic Lie groups 11F70 - Representation-theoretic methods; automorphic representations over local and global fields |