A representation stability theorem for VI-modules

TL;DR

This paper proves that sequences of representations derived from finitely generated VI-modules over algebraically closed fields of characteristic zero are stable, providing a new understanding of their long-term behavior.

Contribution

It establishes a representation stability theorem for VI-modules, a significant advancement in understanding their asymptotic properties.

Findings

Sequences from finitely generated VI-modules are representation stable.

The stability holds over algebraically closed fields of characteristic zero.

Provides a framework for analyzing the asymptotic behavior of these representations.

Abstract

A VI-module gives rise to a sequence of representations of the finite general linear groups. We prove that the sequence obtained from any finitely generated VI-module over an algebraically closed field of characteristic zero is representation stable.