分支图上的sl（2）算子和Markov过程
sl(2) Operators and Markov Processes on Branching Graphs
摘要：
我们提出了一个统一的方法，以各种例子马尔可夫动力学的分区研究Borodin，Olshanski，Fulman，和作者。我们的技术推广了Kerov算子首次出现在[Okounkov，arXiv：math/0002135]，也源于[Fomin，1994]中对分次图的对偶性的研究。我们的主要对象是一个可数分支图携带一个特殊类型的sl（2，C）-模。使用这种结构，我们介绍了区分概率测度的地板上的图形，并定义了两个相关类型的马尔可夫动态与这些措施。我们研究了动力学的谱性质，我们的主要结果是显式描述的马尔可夫生成器的过程之一的特征函数。对于Young图，我们的方法重建了Borodin和Olshanski [arXiv：math-ph/0409075，arXiv：0706.1034]研究的分区上的z-测度和相关动力学。[arXiv：math-ph/0409075]的动力学的生成器在Olshanski [arXiv：1009.2037，arXiv：1103.5848]最近引入的Meixner对称函数的基础上是对角的。我们对这两篇文章的一些结果给出了新的证明。我们的技术适用的其他图形包括杨辉三角形，金曼图（与两个参数的泊松-狄利克雷措施），舒尔图和一般的杰克边多重性的杨图。
英文摘要：
We present a unified approach to various examples of Markov dynamics on partitions studied by Borodin, Olshanski, Fulman, and the author. Our technique generalizes the Kerov's operators first appeared in [Okounkov, arXiv:math/0002135], and also stems from the study of duality of graded graphs in [Fomin, 1994]. Our main object is a countable branching graph carrying an sl(2,C)-module of a special kind. Using this structure, we introduce distinguished probability measures on the floors of the graph, and define two related types of Markov dynamics associated with these measures. We study spectral properties of the dynamics, and our main result is the explicit description of eigenfunctions of the Markov generator of one of the processes. For the Young graph our approach reconstructs the z-measures on partitions and the associated dynamics studied by Borodin and Olshanski [arXiv:math-ph/0409075, arXiv:0706.1034]. The generator of the dynamics of [arXiv:math-ph/0409075] is diagonal in the basis of the Meixner symmetric functions introduced recently by Olshanski [arXiv:1009.2037, arXiv:1103.5848]. We give new proofs to some of the results of these two papers. Other graphs to which our technique is applicable include the Pascal triangle, the Kingman graph (with the two-parameter Poisson-Dirichlet measures), the Schur graph and the general Young graph with Jack edge multiplicities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
