Intertwining of simple characters in GL(n)

Let $F$ be a non-Archimedean local field and let $G$ be the general linear group $G = \text{\rm GL}_n(F)$. Let $θ_1$, $θ_2$ be simple characters in $G$. We show that $θ_1$ intertwines with $θ_2$ if and only if $θ_1$ is endo-equivalent to $θ_2$. We also show that any simple character in $G$ is a $G$-type.

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