Orthogonal polynomial duality of a two-species asymmetric exclusion process

Abstract

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 ${\mathcal{U}}_q({\mathfrak{so}}_6)$ and ${\mathcal{U}}_q({\mathfrak{so}}_8)$. 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.

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Cited by in corpus (1)

• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations