论文标题
MacDonald多项式和扩展的Gelfand-Tsetlin图
Macdonald polynomials and extended Gelfand-Tsetlin graph
论文作者
论文摘要
Using Okounkov's $q$-integral representation of Macdonald polynomials we construct an infinite sequence $Ω_1,Ω_2,Ω_3,\dots$ of countable sets linked by transition probabilities from $Ω_N$ to $Ω_{N-1}$ for each $N=2,3,\dots$.集合$ω_n$的元素是扩展的Gelfand-Tsetlin图的顶点，并且过渡概率取决于两个MacDonald参数，即$ Q $和$ t $。这些数据决定了马尔可夫连锁店的家族，主要结果是其入口边界的描述。这项工作起源于渐近表示理论。在随后的论文中，主要结果适用于$（q，t）$ - 变形$ n $ n $ - 零件β-元素的大$ n $限制过渡。
Using Okounkov's $q$-integral representation of Macdonald polynomials we construct an infinite sequence $Ω_1,Ω_2,Ω_3,\dots$ of countable sets linked by transition probabilities from $Ω_N$ to $Ω_{N-1}$ for each $N=2,3,\dots$. The elements of the sets $Ω_N$ 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.
