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arXiv · 2412.19574

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

Victor Mishnyakov
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Abstract

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.

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Victor Mishnyakov. 2024-12-27. Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials. https://arxiv.org/abs/2412.19574

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