Explicit Hilbert spaces for certain unipotent representations

DOI10.1007/BF01231340zbMath0779.22006OpenAlexW4238299303MaRDI QIDQ1209142

Siddhartha Sahi

Publication date: 16 May 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144058

zbMATH Keywords

universal covering groupinduced representationsparabolic subgroupunipotent representationsHarish-Chandra modulesunitarizabilityautomorphism groups of symmetric tube domains

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Induced representations for locally compact groups (22D30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis in matrix space and Speh's representations
• Singular unitary representations of classical groups
• Whittaker vectors and associated varieties
• On some semi-spherical representations of an Hermitian symmetric pair of the tubular type. II: Construction of the unitary representations
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Wave and Dirac operators, and representations of the conformal group
• The Capelli identity, tube domains, and the generalized Laplace transform
• Unitary representations of Lie groups and operators of finite rank
• Realization of Hermitian symmetric spaces as generalized half-planes
• Unitary Representations of Reductive Lie Groups. (AM-118)
• The Analytic Continuation of the Discrete Series. II