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Globalization of Distinguished Supercuspidal Representations of $\GL(n)$

  Published:2002-06-01
 Printed: Jun 2002
  • Jeffrey Hakim
  • Fiona Murnaghan
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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, 22E35, 11F70 show english descriptions Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Analysis on $p$-adic Lie groups
Representation-theoretic methods; automorphic representations over local and global fields
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
 

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