  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.
