Generating functions associated to highest weight representations

DOI10.1080/10652460500110255zbMath1116.46020OpenAlexW2154958501MaRDI QIDQ5717570

Mark G. Davidson

Publication date: 10 January 2006

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460500110255

zbMATH Keywords

generating functionshighest weight representationsreproducing kernel Hilbert spacesintegral operators

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Semisimple Lie groups and their representations (22E46) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Cites Work

• Unnamed Item
• Hermitian symmetric spaces and their unitary highest weight modules
• Operator-valued positive definite kernels on tubes
• Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials.
• Laguerre polynomials, restriction principle, and holomorphic representations of SL\((2\mathbb R)\)
• The generalized Segal--Bargmann transform and special functions
• Differential recursion relations for Laguerre functions on Hermitian matrices

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