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Let $k$ be a local field and $n \in \mathbb{N}$. Question: I would like to know precisely, which irreducible (admissible) representations of $G := \textrm{GL}_n(k)$ are generic, i.e. which admit ...

$\DeclareMathOperator\Kern{Kern}\DeclareMathOperator\GL{GL}\DeclareMathOperator\C{\mathbb{C}}\DeclareMathOperator\Z{\mathbb{Z}}\DeclareMathOperator\diag{diag}\DeclareMathOperator\Ind{Ind}\newcommand\...