The Type D asymmetric simple exclusion process (Type D ASEP) is a two-species interacting particle system exhibiting a drift, where two particles may occupy the same site only if they belong to different species. In previous research (arXiv:2011.13473), the Type D ASEP was generated using the quantum Hamiltonian corresponding to central elements from the quantum groups $\mathcal{ U}_q(\mathfrak{ so}_6)$ and $\mathcal{ U}_q(\mathfrak{ so}_8)$. We extend this construction to the case of $\mathcal{ U}_q(\mathfrak{ so}_{ 10})$. Additionally, we generalize a previously known duality function from arXiv:2209.11114 for the Type D ASEP for all $n$.
Categories: math.PR math-ph math.MP