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

TL;DR

This paper extends the algebraic construction of a two-species particle system called Type D ASEP to a higher-rank quantum group, providing new duality functions and deepening the algebraic understanding of these stochastic processes.

Contribution

The paper introduces a new construction of Type D ASEP using $_q(_{10})$, expanding previous work from lower-rank quantum groups, and generalizes duality functions for all system sizes.

Findings

Extended the algebraic framework to $_q(_{10})$.

Generalized duality functions for all system sizes.

Provided new insights into the algebraic structure of Type D ASEP.

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 $n$.