VI modules in non-describing characteristic, Part II

Abstract

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