一个奇特的五顶点模型与环上的多物种ASEP
A strange five vertex model and multispecies ASEP on a ring
AI总结：
本文通过引入具有奇特权守恒的量子振子加权五顶点模型，研究了一维周期格子上多物种ASEP的稳态构造，阐明了多项已知结果的关联并细化了其推导。
摘要：
我们重新审视了在一维周期格子上构造多物种不对称简单排他过程（ASEP）稳态的问题。我们方法的核心是一个量子振子加权的五顶点模型，它具有一种不同于传统守恒的奇特权守恒。我们的结果阐明了若干已知结果之间的相互关系，并细化了它们的推导。例如，由Martin（2020）和Corteel--Mandelshtam--Williams（2022）通过多行队列构造导出的稳态概率被等同于一个三维系统的配分函数。Prolhac--Evans--Mallick（2009）提出的矩阵乘积算子获得了作为角转移矩阵（CTM）的自然图示解释。正如Aggarwal--Nicoletti--Petrov（2023）所质疑的，其递归张量结构的起源通过CTM图被揭示。最后，通过阐明其与源自量子群表示的Yang--Baxter方程解的精确联系，Cantini--de Gier--Wheeler（2015）对Zamolodchikov--Faddeev代数的推导被内化。
英文摘要：
We revisit the problem of constructing the stationary states of the multispecies asymmetric simple exclusion process on a one-dimensional periodic lattice. Central to our approach is a quantum oscillator weighted five vertex model which features a strange weight conservation distinct from the conventional one. Our results clarify the interrelations among several known results and refine their derivations. For instance, the stationary probability derived from the multiline queue construction by Martin (2020) and Corteel--Mandelshtam--Williams (2022) is identified with the partition function of a three-dimensional system. The matrix product operators by Prolhac--Evans--Mallick (2009) acquire a natural diagrammatic interpretation as corner transfer matrices (CTM). The origin of their recursive tensor structure, as questioned by Aggarwal--Nicoletti--Petrov (2023), is revealed through the CTM diagrams. Finally, the derivation of the Zamolodchikov--Faddeev algebra by Cantini--de Gier--Wheeler (2015) is made intrinsic by elucidating its precise connection to a solution to the Yang--Baxter equation originating from quantum group representations.
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