A geometric quantization of the Kostant-Sekiguchi correspondence for scalar type unitary highest weight representations

zbMath1277.22011arXiv1205.5171MaRDI QIDQ374016

Jan Möllers

Publication date: 25 October 2013

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

Full work available at URL: https://arxiv.org/abs/1205.5171

zbMATH Keywords

Bessel operatorBessel functionJordan algebraorbit methodbranching lawFock modelSchrödinger modelSegal-Bargmann transformunitary highest weight representationunitary inversion operatorWhittaker vectors

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Other hypergeometric functions and integrals in several variables (33C70) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Bergman spaces and Fock spaces (30H20) Associated groups, automorphisms of Jordan algebras (17C30)

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The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula ⋮ Hankel transform, \(\mathcal{K}\)-Bessel functions and zeta distributions in the Dunkl setting ⋮ Unnamed Item ⋮ Bessel operators on Jordan pairs and small representations of semisimple Lie groups

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