Geodesic
Generic Smooth Representations
Documenta mathematica, Tome 25 (2020), pp. 2473-2485
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Let F be a non-archimedean local field. In this paper we explore genericity of irreducible smooth representations of GLn​(F) by restriction to a maximal compact subgroup K of GLn​(F). Let (J,λ) be a Bushnell-Kutzko type for a Bernstein component Ω. The work of Schneider-Zink gives an irreducible K-representation σmin​(λ), which appears with multiplicity one in IndJK​λ. Let π be an irreducible smooth representation of GLn​(F) in Ω. We will prove that π is generic if and only if σmin​(λ) is contained in π, in which case it occurs with multiplicity one.
DOI : 10.4171/dm/804
Classification : 11F70, 11F85, 22E50
Mots-clés : representations, p-adic groups 
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     author = {Alexandre Pyvovarov},
     title = {Generic {Smooth} {Representations}},
     journal = {Documenta mathematica},
     pages = {2473--2485},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/804},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/804/}
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Alexandre Pyvovarov. Generic Smooth Representations. Documenta mathematica, Tome 25 (2020), pp. 2473-2485. doi: 10.4171/dm/804

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