Representation stability of power sets and square free polynomials

TL;DR

This paper studies how the symmetric group representations on power sets and square-free polynomials stabilize as the set size grows, with applications to the cohomology of pure braid groups.

Contribution

It introduces a stability analysis of symmetric group actions on power sets and square-free polynomials, linking these to cohomological representations.

Findings

Representation stability established for power sets and square-free polynomials

Application to symmetric group action on pure braid group cohomology

Insights into the structure of related algebraic representations

Abstract

The symmetric group acts on the power set and also on the set of square free polynomials. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the cohomology of the pure braid group.