New superintegrability formulas are proposed for eigenvalue models built on multivariate Meixner-Pollaczek and Wilson measures, with the Wilson case left partly conjectural.
Hermitian Symmetric Spaces of Tube Type and Multivariate Meixner-Pollaczek Polynomials
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abstract
Harmonic analysis on Hermitian symmetric spaces of tube type is a natural framework for introducing multivariate Meixner-Pollaczek polynomials. Their main properties are established in this setting: generating and determinantal formulae, difference equations. As an application we consider the problem of evaluating moments related to a multivariate Barnes type integral involving the Harish-Chandra $c$-function of a symmetric cone.
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Superintegrability of the Wilson family of matrix models and moments of multivariable orthogonal polynomials
New superintegrability formulas are proposed for eigenvalue models built on multivariate Meixner-Pollaczek and Wilson measures, with the Wilson case left partly conjectural.