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arXiv · 2307.15660

A Type D Asymmetric Simple Exclusion Process Generated by an Explicit Central Element of $\mathcal{U}_q(\mathfrak{so}_{10})$

Eddie Rohr·Karthik Sellakumaran Latha·Amanda Yin
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Abstract

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 $n$.

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Eddie Rohr, Karthik Sellakumaran Latha, Amanda Yin. 2023-07-28. A Type D Asymmetric Simple Exclusion Process Generated by an Explicit Central Element of $\mathcal{U}_q(\mathfrak{so}_{10})$. https://arxiv.org/abs/2307.15660

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