Typical representations for level zero Bernstein components of ${\mathrm{GL}}_n(F)$

Abstract

Let $F$ be a non-discrete non-Archimedean locally compact field. In this article for a level zero Bernstein component $s$, we classify those irreducible smooth representations of ${\rm GL}_n{\integers{F}}$ (called typical representations) whose appearance in a smooth irreducible representation $\pi$ of ${\mathrm{GL}}_{n}F$ implies that the cuspidal support of $\pi$ is $s$. These results extend, for level zero representations, the results of Henniart and Paškūnas on cuspidal representations. The results are independent of the characteristic of the base field.

Appeared in Journal of algebra