Equivariant unimodality conjecture for inverse Z-polynomials of matroids

Let $\mathrm{M}$ be a matroid equipped with an action of a finite group $W$. Its equivariant inverse $Z$-polynomial has coefficients that are virtual representations of $W$; a sequence of such representations is equivariantly unimodal if it increases and then decreases with respect to the representation-order relation.

Equivariant unimodality conjecture. For any matroid $\mathrm{M}$ equipped with an action of a finite group $W$, the coefficients of its equivariant inverse $Z$-polynomial are equivariantly unimodal.

The conjecture is confirmed in the paper for uniform matroids. The general case remains open.