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GH from MO
GH from MO
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Let $G=GL(n,F)$, where $F$ is a non archimidian-archimedean local field. If we consider a smooth representation $\pi$ of $G$ such that evreyevery irreducible generic representationsrepresentation of $G$ embeds in $\pi$, is it true that the representation $Ind_U^G\chi$ embeds in $\pi$, where $U$ is the standard unipotent subgroup of $G$ and $\chi$ is any fixed non degenerate-degenerate caracter of $U$  ?

Let $G=GL(n,F)$, where $F$ a non archimidian local field. If we consider a smooth representation $\pi$ of $G$ such that evrey irreducible generic representations of $G$ embeds in $\pi$, is that the representation $Ind_U^G\chi$ embeds in $\pi$, where $U$ is the standard unipotent subgroup of $G$ and $\chi$ any fixed non degenerate caracter of $U$  ?

Let $G=GL(n,F)$, where $F$ is a non-archimedean local field. If we consider a smooth representation $\pi$ of $G$ such that every irreducible generic representation of $G$ embeds in $\pi$, is it true that the representation $Ind_U^G\chi$ embeds in $\pi$, where $U$ is the standard unipotent subgroup of $G$ and $\chi$ is any fixed non-degenerate caracter of $U$?

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Rajkarov
Rajkarov
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Generic representations of $GL(n,F)$

Let $G=GL(n,F)$, where $F$ a non archimidian local field. If we consider a smooth representation $\pi$ of $G$ such that evrey irreducible generic representations of $G$ embeds in $\pi$, is that the representation $Ind_U^G\chi$ embeds in $\pi$, where $U$ is the standard unipotent subgroup of $G$ and $\chi$ any fixed non degenerate caracter of $U$ ?