Distinguished Representations of $\mathrm{GL}_{n}(\mathbb{F}_{q})$ (2205.00987v1)

Abstract: Let $\mathrm{G} = \mathrm{Gl}{n}(K)$, and $\mathrm{H} = \mathrm{G}^{\sigma}$ for $\sigma$ an involution of the form $g\rightarrow aga^{-1}$, It is known that for $K =\mathbb{Q}_q$ any irreducible representation of $\mathrm{G}$ with an $\mathrm{H}$ invariant functional, is self dual, we prove an analogous result for $\mathbb{F}{q}$.