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Orthogonal Polynomials in Mathematical Physics
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abstract
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal polynomials and consider their various generalizations. The review also includes the orthogonal polynomials into a generic framework of ($q$-)hypergeometric functions and their integral representations. In particular, this gives rise to relations with conformal blocks of the Virasoro algebra.
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Cited by 1 Pith paper
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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.
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