Berezin kernels and analysis on Makarevich spaces

DOI10.1016/S0019-3577(05)80036-9zbMath1138.43009arXivmath/0411294OpenAlexW1985123345MaRDI QIDQ855596

Michael Pevzner, Jacques Faraut

Publication date: 7 December 2006

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411294

zbMATH Keywords

canonical representationsBerezin kernelsJordan algebrasRiemannian symmetric spaces

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46)

Related Items (5)

The Berezin form on symmetric $R$-spaces and reflection positivity ⋮ Branching laws for discrete Wallach points ⋮ Reflection positivity on spheres ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ Intertwining operators for the generalized principal series on a symmetric 𝑅-space

Cites Work

• Explicit Hilbert spaces for certain unipotent representations
• Berezin transform on compact Hermitian symmetric spaces
• Tensor products of maximal degenerate series representations of the group \(SL(n,\mathbb{R})\)
• Canonical representations related to hyperbolic spaces
• Algebraic structures of Makarevič spaces. I
• Harmonic analysis on vector bundles over \(\text{Sp}(1,n)/\text{Sp}(1)\times\text{Sp}(n)\)
• Plancherel formula for Berezin deformation of \(L^{2}\) on Riemannian symmetric space
• Jordan algebras and generalized principal series representations
• The Berezin transform and invariant differential operators
• Berezin transform on real bounded symmetric domains
• QUANTIZATION
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• A mean value theorem on bounded symmetric domains
• Matrix analogues of the beta function and Plancherel's formula for Berezin kernel representations
• Jordan algebras and degenerate principal series.
• Analyse conforme sur les algèbres de Jordan
• Berezin kernels of tube domains
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