VI modules in non-describing characteristic, Part II

We classify all irreducible generic $\mathrm{V}\mathrm{I}$-modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic $\mathrm{F}\mathrm{I}$-modules in arbitrary characteristic. Our result can also be viewed as a classification theorem for a natural class of representations of ${\mathbf{G}\mathbf{L}}_{\mathrm{\infty }}({\mathbf{F}}_q)$.