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Title: Generic smooth representations
Speaker: Dr. Alexandre Pyvovarov (MCM)
Time: 2020-12-17, 10:30-11:30am
Place: MCM110;&;ZOOM;(Zoom;ID:;466;356;2952;;Password:;mcm1234)
Abstract: Let F be a non-archimedean local field. In this talk we will 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 IndKJλ. 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.
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