Unimodality conjecture for dominant affine Bruhat intervals

Let $t_\lambda$ be the affine Weyl group element associated with the dominant coweight $\lambda$, and let $f$ denote the finite Weyl group element used to define the dominant lower Bruhat interval. For each rank $i$, let $b_i^{t_\lambda,f}$ denote the number of elements of length $i$ in this interval. Unimodality conjecture. The sequence $\{b_i^{t_\lambda,f}\}$ is unimodal.

This is the discrete analogue of the paper's asymptotic log-concavity result for dominant lower Bruhat intervals. The source presents it as the main conjecture and suggests that it may be difficult to prove; its resolution is not supplied.