VI-modules in non-describing characteristic, part II

Abstract

Abstract We classify all irreducible generic VI {\mathrm{VI}} -modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic FI {\mathrm{FI}} -modules in arbitrary characteristic. Equivalently, we provide a complete classification of irreducibles of admissible 𝐆𝐋 ∞ ⁢ ( 𝔽 q ) {\mathbf{GL}_{\infty}(\mathbb{F}_{q})} -representations in non-describing characteristic, which is new even in characteristic zero. This result degenerates to provide a complete classification of irreducibles of admissible S ∞ {S_{\infty}} -representations in arbitrary characteristic, which is new away from characteristic zero.