对称椭圆函数、IRF模型和动态排斥过程
Symmetric elliptic functions, IRF models, and dynamic exclusion processes
摘要：
我们引入了与椭圆量子群$E_{τ,η}(sl_2)$的表示相关的随机交互-Round-a-Face（IRF）模型。随机IRF模型在一个象限中，我们评估的平均值为一个广泛的家庭，可以被看作是更高的类似物的$q$ -矩的高度函数的随机（更高的自旋）六顶点模型的观测。在一定的限制下，随机IRF模型退化为（1+1）d相互作用粒子系统，我们称之为动态ASEP和SSEP，它们的跳跃率依赖于高度函数的局部值。对于阶跃初始条件，我们也计算了它们的可观测量的平均值，并使用它们来研究动态SSEP的一点渐近性。的建设和证明是基于显着的属性（分支和Pieri规则，柯西身份）的一个（看似新的）家庭的对称椭圆函数，出现作为矩阵元素在一个无限的体积限制的代数Bethe anomaly的$E_{τ,η}(sl_2)$。
英文摘要：
We introduce stochastic Interaction-Round-a-Face (IRF) models that are related to representations of the elliptic quantum group $E_{τ,η}(sl_2)$. For stochasic IRF models in a quadrant, we evaluate averages for a broad family of observables that can be viewed as higher analogs of $q$-moments of the height function for the stochastic (higher spin) six vertex models. In a certain limit, the stochastic IRF models degenerate to (1+1)d interacting particle systems that we call dynamic ASEP and SSEP; their jump rates depend on local values of the height function. For the step initial condition, we evaluate averages of observables for them as well, and use those to investigate one-point asymptotics of the dynamic SSEP. The construction and proofs are based on remarkable properties (branching and Pieri rules, Cauchy identities) of a (seemingly new) family of symmetric elliptic functions that arise as matrix elements in an infinite volume limit of the algebraic Bethe ansatz for $E_{τ,η}(sl_2)$.
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