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 [15], using the type D quantum groups U-q(so(6)) and U-q(so(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.