标题： 威尔逊矩阵模型族的超可积性及多变量正交多项式的矩 显示英文标题

标题： Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials

摘要： 我们提出了超可积矩阵/特征值模型的新例子。 这些例子是通过探索超可积性理论与多元正交多项式之间关系的结果而产生的。 新的超可积例子建立在Meixner-Pollaczek和Wilson多项式的多元推广及其相应测度的基础上。 从多元正交多项式的角度来看，本文提出了相应多变量测度的（广义）矩的表达式。 从超可积性的角度来看，我们揭示了一些新的现象，例如作为无任何变形的超可积基的Schur多项式的偏离，以及答案中出现的新组合结构。 显示英文摘要

摘要： We present new examples of superintegrable matrix/eigenvalue models. These examples arise as a result of the exploration of the relationship between the theory of superintegrability and multivariate orthogonal polynomials. The new superintegrable examples are built upon the multivariate generalizations of the Meixner-Pollaczek and Wilson polynomials and their respective measures. From the perspective of multivariate orthogonal polynomials in this work we propose expressions for (generalized) moments of the respective multi-variable measures. From the perspective of superintegrability we uncover a couple of new phenomena such as the deviation from Schur polynomials as the superintegrable basis without any deformation and new combinatorial structures appearing in the answers.