Equivariant -positivity of Chow rings and augmented Chow rings of matroids

In this paper, we prove the Chow ring and augmented Chow ring of a matroid is equivariant -positivity under the action of any group of automorphisms of the matroid. This verifies a conjecture of Angarone, Nathanson, and Reiner. Our method gives an explicit interpretation to the coefficients of the equivariant -expansion. Applying our theorem to uniform matroids, we extend and recover several known results regarding uniform matroids and Eulerian quasisymmetric functions. Using these results, we are able to answer a problem proposed by Athanasiadis about extending the -expansion of the binomial Eulerian polynomial.