Explicit Hilbert spaces for certain unipotent representations. III

DOI10.1016/S0022-1236(03)00069-7zbMath1029.22021arXivmath/0110339OpenAlexW2887648212MaRDI QIDQ1402319

Siddhartha Sahi, Alexander Dvorsky

Publication date: 20 August 2003

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110339

zbMATH Keywords

Jordan algebraSpherical vectorUnipotent representation

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Associated groups, automorphisms of Jordan algebras (17C30)

Related Items

Minimal representations of simple real Lie groups of non Hermitian type, Zeta distributions and boundary values of Poisson transforms, Heisenberg parabolically induced representations of Hermitian Lie groups, part I: Intertwining operators and Weyl transform, Structure of the degenerate principal series on symmetric \(R\)-spaces and small representations, Bessel operators on Jordan pairs and small representations of semisimple Lie groups, Minimal representations via Bessel operators, Covariant quantization: spectral analysis versus deformation theory

Cites Work

• Hyperfunctions and harmonic analysis on symmetric spaces
• Analysis in matrix space and Speh's representations
• Singular unitary representations of classical groups
• Tensor products of singular representations and an extension of the \(\theta\)-correspondence
• Explicit Hilbert spaces for certain unipotent representations
• Jordan algebras and Capelli identities
• Explicit Hilbert spaces for certain unipotent representations. II
• Unitary representations of Lie groups and operators of finite rank
• Generalized Bessel functions on symmetric spaces
• Jordan algebras and degenerate principal series.
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