Using Okounkov’s q-integral representation of Macdonald polynomials we construct an infinite sequence \(\Omega _1,\Omega _2,\Omega _3,\dots \) of countable sets linked by transition probabilities from \(\Omega _N\) to \(\Omega _{N-1}\) for each \(N=2,3,\dots \). The elements of the sets \(\Omega _N\) are the vertices of the extended Gelfand–Tsetlin graph, and the transition probabilities depend on the two Macdonald parameters, q and t. These data determine a family of Markov chains, and the main result is the description of their entrance boundaries. This work has its origin in asymptotic representation theory. In the subsequent paper, the main result is applied to large-N limit transition in (q, t)-deformed N-particle beta-ensembles.

使用Macdonald 多项式的Okounkov 的q积分表示，我们构建了一个无限序列\(\Omega _1,\Omega _2,\Omega _3,\dots \)的可数集，由从\(\Omega _N\)到\( \Omega _{N-1}\)对于每个\(N=2,3,\dots \)。集合\(\Omega _N\)的元素是扩展的 Gelfand-Tsetlin 图的顶点，转移概率取决于两个 Macdonald 参数q和t. 这些数据确定了一系列马尔可夫链，主要结果是对它们入口边界的描述。这项工作起源于渐近表示理论。在随后的论文中，主要结果应用于( q ,  t ) 变形N粒子 β 系综中的大N极限跃迁。