Limit transition between hypergeometric functions of type BC and type A

DOI10.1112/S0010437X13007045zbMath1405.33019arXiv1207.0487MaRDI QIDQ2852245

Koornwinder, Tom H., Michael Voit, Margit Rösler

Publication date: 8 October 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.0487

zbMATH Keywords

spherical functionsGrassmann manifoldslimit transitionsHeckman-Opdam theoryhypergeometric functions associated with root systemsOlshanski spherical pairs

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Differential geometry of symmetric spaces (53C35) Harmonic analysis and spherical functions (43A90) Hypergeometric functions associated with root systems (33C67) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (9)

The Dunkl-Laplace transform and Macdonald’s hypergeometric series ⋮ Central limit theorems for random walks associated with hypergeometric functions of type BC ⋮ Sonine Formulas and Intertwining Operators in Dunkl Theory ⋮ Dispersion and limit theorems for random walks associated with hypergeometric functions of type \(BC\) ⋮ Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ An Introduction to Dunkl Theory and Its Analytic Aspects ⋮ Integral representation and uniform limits for some Heckman-Opdam hypergeometric functions of type \textsl{BC} ⋮ Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions

Cites Work

• Infinite-dimensional classical groups of finite \(r\)-rank: description of representations and asymptotic theory
• Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC
• The Calogero-Sutherland model and generalized classical polynomials
• Some combinatorial properties of Jack symmetric functions
• Harmonic analysis for certain representations of graded Hecke algebras
• Contributions to the hypergeometric function theory of Heckman and Opdam: Sharp estimates, Schwartz space, heat kernel
• An elementary approach to the hypergeometric shift operators of Opdam
• Limit Transitions for BC Type Multivariable Orthogonal Polynomials

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