Equivariant log concavity and representation stability

Abstract

We expand upon the notion of equivariant log concavity, and make equivariant log concavity conjectures for Orlik--Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik--Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra ${\mathfrak{sl}}_n$, we exploit the theory of representation stability to give computer assisted proofs of these conjectures in low degree.