Virtual Specht stability for $FI$-modules in positive characteristic

TL;DR

This paper introduces the concept of virtual Specht stability as a relaxed form of representation stability for symmetric group representations, demonstrating its presence in $FI$-modules over fields of positive characteristic.

Contribution

It defines virtual Specht stability and proves that $FI$-modules over fields of positive characteristic exhibit this stability, extending understanding of representation stability.

Findings

$FI$-modules over positive characteristic fields show virtual Specht stability

Virtual Specht stability generalizes the Church-Farb notion of stability

Structural results of Nagpal are used to establish the main theorem

Abstract

We define a notion of virtual Specht stability which is a relaxation of the Church-Farb notion of representation stability for sequences of symmetric group representations. Using a structural result of Nagpal, we show that $FI$-modules over fields of positive characteristic exhibit virtual Specht stability.