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Let $F$ be a non-Archimedean local field and let $G$ be the general lineargroup $G = \text{\rm GL}_n(F)$. Let $\theta_1$, $\theta_2$ be simple charactersin $G$. We show that $\theta_1$ intertwines with $\theta_2$ if and only if$\theta_1$ is endo-equivalent to $\theta_2$. We also show that any simplecharacter in $G$ is a $G$-type.

Intertwining of simple characters in GL(n)