多物种TASEP和组合$R$
Multispecies TASEP and combinatorial $R$
摘要：
利用晶体基础理论中量子仿射代数$U_q(\widehat{sl}_L)$的组合$R$的合成，给出了Ferrari和Martin在$L$格点周期链上构造$n$ -物种完全不对称简单排斥过程（TASEP）稳态的算法.基于这种联系和最近从四面体方程导出的$R$矩阵的因式分解形式，我们建立了一个新的TASEP稳态的矩阵乘积公式，该公式用$q=0$上的$q$振子值五顶点模型的角转移矩阵表示。
英文摘要：
We identify the algorithm for constructing steady states of the $n$-species totally asymmetric simple exclusion process (TASEP) on $L$ site periodic chain by Ferrari and Martin with a composition of combinatorial $R$ for the quantum affine algebra $U_q(\widehat{sl}_L)$ in crystal base theory. Based on this connection and the factorized form of the $R$ matrix derived recently from the tetrahedron equation, we establish a new matrix product formula for the steady state of the TASEP which is expressed in terms of corner transfer matrices of the $q$-oscillator valued five-vertex model at $q=0$.
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