  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 $\mathbb{F}_{q}$.
