Unimodality conjecture for typical weight multiplicity polynomials of $\mathfrak{gl}(n,m)$

Let $P^+(n,m)$ be the set of dominant weights, let $\rho$ be the relevant Weyl vector, and let $K_{\lambda,\mu}(q)$ denote the $q$-analog of the weight multiplicity for $\mathfrak{gl}(n,m)$. A dominant weight $\lambda$ is typical when it is typical in the sense of Lie superalgebra representation theory. Unimodality conjecture. For any typical dominant weight $\lambda$ and any $\mu\in P^+(n,m)$, the polynomial $K_{\lambda,\mu}(q)$ is unimodal. This conjecture is based on computational experiments with the $q$-analogs; its general validity is not established in the source.