Orthogonal polynomial duality of a two-species asymmetric exclusion process

We examine type D ASEP, a two–species interacting particle system which generalizes the usual asymmetric simple exclusion process. For certain cases of type D ASEP, the process does not give priority for one species over another, even though there is nontrivial interaction between the two species. For those specific cases, we prove that the type D ASEP is self–dual with respect to an independent product of $q$–Krawtchouk polynomials. The type D ASEP was originally constructed in arXiv:2011.13473, using the type D quantum groups ${\mathcal{U}}_q({\mathfrak{s}\mathfrak{o}}_6)$ and ${\mathcal{U}}_q({\mathfrak{s}\mathfrak{o}}_8)$. That paper claimed that certain states needed to be "discarded’’ in order to ensure non–negativity. Here, we also provide a more efficient argument for the same claim.