Multivariate Jacobi polynomials and the Selberg integral. II

DOI10.1007/s10958-016-2881-3zbMath1347.43004OpenAlexW2345534209MaRDI QIDQ2628947

A. A. Osinenko, Grigori Olshanski

Publication date: 19 July 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-016-2881-3

zbMATH Keywords

symmetric polynomialsLebesgue measurestochastic matrixcomplex measuresSelberg integralmultivariate Jacobi polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Orthogonal polynomials and functions associated with root systems (33C52)

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Cites Work

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• Multivariate Jacobi polynomials and the Selberg integral
• A quantization of the harmonic analysis on the infinite-dimensional unitary group
• Determinantal measures related to big \(q\)-Jacobi polynomials
• Measures on infinite dimensional Grassmann manifolds
• The Selberg-Jack symmetric functions
• The problem of harmonic analysis on the infinite-dimensional unitary group.
• Anisotropic Young diagrams and Jack symmetric functions
• Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities.
• A duality of MacDonald-Koornwinder polynomials and its application to integral representations
• Hua-type integrals over unitary groups and over projective limits of unitary groups
• Harmonic functions on multiplicative graphs and interpolation polynomials
• BC\(_n\)-symmetric polynomials
• The importance of the Selberg integral
• The Young bouquet and its boundary

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