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 $U$ ?