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Let $F$ be a non-discrete non-Archimedean locally compact field. In thisarticle for a level zero Bernstein component $s$, we classify those irreduciblesmooth representations of ${\rm GL}_n{\integers{F}}$ (called typicalrepresentations) whose appearance in a smooth irreducible representation $\pi$of ${\rm GL}_n{F}$ implies that the cuspidal support of $\pi$ is $s$. Theseresults extend, for level zero representations, the results of Henniart andPa\v{s}k\={u}nas on cuspidal representations. The results are independent ofthe characteristic of the base field.

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