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Globalization of Distinguished Supercuspidal Representations of GL(n)

Published online by Cambridge University Press:  20 November 2018

Jeffrey Hakim  and
Fiona Murnaghan
Jeffrey Hakim
Affiliation:
Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue NW, Washington, DC 20016, U.S.A., e-mail: jhakim@american.edu
Fiona Murnaghan
Affiliation:
Department of Mathematics, University of Toronto, 100 Saint George Street, Toronto, Ontario, M5S 3G3, e-mail: fiona@math.toronto.edu
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Abstract

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An irreducible supercuspidal representation $\pi$ of $G\,=\,\text{GL}\left( n,\,F \right)$, where $F$ is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup $H$ of $G$ and a quasicharacter $\text{ }\!\!\chi\!\!\text{ }$ of $H$ if $\text{Ho}{{\text{m}}_{H}}\left( \pi ,\,\text{ }\!\!\chi\!\!\text{ } \right)\,\ne \,0$. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to $\text{GL}\left( n \right)$. 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.

Keywords

22E5022E3511F70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 220 - 230
Copyright
Copyright © Canadian Mathematical Society 2002

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