Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic smooth representations   Let $F$ be a non-archimedean local field. In this paper we 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 $\pi$ with
multiplicity one.

28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat