On Certain Degenerate Whittaker Models for Cuspidal Representations of ${\mathrm{GL}}_{k\cdot n}\left({\mathbb{F}}_q\right)$

Ofir Gorodetsky, Zahi Hazan

Let $\pi$ be an irreducible cuspidal representation of ${\mathrm{GL}}_{kn}\left({\mathbb{F}}_q\right)$. Assume that $\pi ={\pi }_{\theta }$, corresponds to a regular character $\theta$ of $\mathbb{F}_{q^{kn…