VI modules in non-describing characteristic, Part II

TL;DR

This paper classifies all irreducible generic modules for the VI category in non-describing characteristic, extending to FI-modules and representations of infinite general linear groups, providing a comprehensive understanding of their structure.

Contribution

It provides a complete classification of irreducible generic VI-modules in non-describing characteristic, linking to FI-modules and infinite general linear group representations.

Findings

Classification of irreducible generic VI-modules in non-describing characteristic

Degeneration to classification of FI-modules in arbitrary characteristic

Application to representations of fGLf_f(F_q)

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 $\mathbf{GL}_{\infty}(\mathbf{F}_q)$.