Intertwining of simple characters in GL(n)

Abstract

Let $F$ be a non-Archimedean local field and let $G$ be the general linear group $G={\text{GL}}_n(F)$. Let ${\theta }_1$, ${\theta }_2$ be simple characters in $G$. 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 simple character in $G$ is a $G$-type.

7 pages

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