Berezin quantization and holomorphic representations

DOI10.4171/RSMUP/129-16zbMath1272.22007MaRDI QIDQ361757

Benjamin Cahen

Publication date: 19 August 2013

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

zbMATH Keywords

unitary representationreductive groupWeyl correspondenceBerezin quantizationStratonovich-Weyl map, quasi-Hermitian Lie group

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (11)

Berezin Symbols on Lie Groups ⋮ A note on the harmonic representation of \(\mathrm{SU}(p,q)\) ⋮ Unnamed Item ⋮ Formal deformations and principal series representations of ${\rm SL}(2,{\mathbb R})$ and ${\rm SL}(2,{\mathbb C})$ ⋮ The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond group ⋮ Unnamed Item ⋮ Invariant symbolic calculus for semidirect products ⋮ Invariant symbolic calculus for compact Lie groups ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Coherent states and Berezin quantization for non-scalar holomorphic representations

Cites Work

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• Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups
• Weyl quantization for principal series
• Berezin quantization for discrete series
• Weyl quantization for semidirect products
• Deformation program for principal series representations
• Contraction of compact semisimple Lie groups via Berezin quantization
• Polarization and unitary representations of solvable Lie groups. Appendix by Calvin C. Moore
• Berezin quantization on generalized flag manifolds
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• Quantification d'une orbite massive d'un groupe de Poincaré généralisé
• QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS

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