Geodesic
Globalization of Distinguished Supercuspidal Representations of GL(n)
Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 220-230

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DOI

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.
DOI : 10.4153/CMB-2002-025-x
Mots-clés : 22E50, 22E35, 11F70 
Hakim, Jeffrey; Murnaghan, Fiona. Globalization of Distinguished Supercuspidal Representations of GL(n). Canadian mathematical bulletin, Tome 45 (2002) no. 2, pp. 220-230. doi: 10.4153/CMB-2002-025-x
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     title = {Globalization of {Distinguished} {Supercuspidal} {Representations} of {GL(n)}},
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