Lecture----数学院晨兴数学中心

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 $GL_n(F)$ by restriction to a maximal compact subgroup $K$ of $GL_n(F)$. Let $(J, \lambda)$ be a Bushnell--Kutzko type for a Bernstein component $\Omega$. The work of Schneider--Zink gives an irreducible $K$-representation $\sigma_{min}(\lambda)$, which appears with multiplicity one in $\mathrm{Ind}_J^K \lambda$. Let $\pi$ be an irreducible smooth representation of $GL_n(F)$ in $\Omega$. We will prove that $\pi$ is generic if and only if $\sigma_{min}(\lambda)$ is contained in $\pi$, in which case it occurs with multiplicity one.
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