若干经典多元分布的高丁模型
Gaudin models for some classical multivariate distributions
AI总结：
该研究针对多元Hahn、Dirichlet、多项及负多项分布，借助表示论工具构造对应Gaudin模型的多元正交多项式，为量子超可积系统理论提供了新的相关结果。
AI中文摘要：
与若干经典多元分布相关的Kohno-Drinfeld李代数表示，在量子超可积系统理论的近期发展中发挥了重要作用。本研究分析了对应于多元Hahn分布、Dirichlet分布、多项分布及负多项分布的Gaudin模型。更确切地说，我们利用表示论工具，构造了关于这些分布的多元正交多项式，使其成为Gaudin算子的共同本征函数。这些多项式由Bethe ansatz方程的解参数化，等价于Heine-Stieltjes多项式的根。
英文摘要：
Representations of the Kohno-Drinfeld Lie algebra associated with several classical multivariate distributions have played an important role in recent developments in the theory of quantum superintegrable systems. In this work, we analyze the corresponding Gaudin models for the multivariate Hahn, Dirichlet, multinomial, and negative multinomial distributions. More precisely, using tools from representation theory, we construct multivariate orthogonal polynomials with respect to these distributions as common eigenfunctions of Gaudin operators. The polynomials are parametrized by solutions to the Bethe ansatz equations or, equivalently, by the roots of Heine-Stieltjes polynomials.
