Intertwining operators into Dolbeault cohomology representations

DOI10.1016/0022-1236(92)90110-5zbMath0761.22015OpenAlexW1984455584MaRDI QIDQ1193912

A. W. Knapp, Roger Zierau, Leticia Barchini

Publication date: 27 September 1992

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

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90110-5

zbMATH Keywords

holomorphic line bundlesemisimple real Lie groupDolbeault cohomology sections

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Homology and cohomology of Lie groups (57T10) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Geometric quantization (53D50)

Related Items

Intertwining operators into cohomology representations for semisimple Lie groups ⋮ Boundary value maps, Szegö maps and intertwining operators ⋮ Unnamed Item ⋮ On the unitary globalization of cohomologically induced modules ⋮ Square integrable harmonic forms and representation theory ⋮ IRREDUCIBLE UNITARY REPRESENTATIONS OF SU_p,q I: THE DISCRETE SERIES ⋮ A twistor correspondence and Penrose transform for odd-dimensional hyperbolic space ⋮ Strongly harmonic forms for representations in the discrete series ⋮ ON HOMOGENEOUS CR MANIFOLDS AND THEIR CR ALGEBRAS ⋮ Principal series representations and harmonic spinors ⋮ Indefinite Harmonic Theory and Harmonic Spinors ⋮ Harmonic spinors on semisimple symmetric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On representations and compactifications of symmetric Riemannian spaces
• Homogeneous vector bundles
• Localization and standard modules for real semisimple Lie groups. I: The duality theorem
• A construction of harmonic forms on \(U(p+1,q)/U(p,q)\times U(1)\)
• The algebraic structure of the representation of semisimple Lie groups. I
• Poincaré series and automorphic cohomology on flag domains
• Correction and addition to Szegö kernels associated with discrete series
• Representations of real reductive Lie groups
• Multiplicity formulae for discrete series
• \(L^2\)-cohomology and the discrete series
• Geometric quantization and derived functor modules for semisimple Lie groups
• Singular unitary representations and indefinite harmonic theory
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Locally homogeneous complex manifolds
• Unitary Representations of Reductive Lie Groups. (AM-118)
• Sur les représentations induites des groupes de Lie
• Cauchy-Szego Maps, Invariant Differential Operators and Some Representations of SU(n + 1, 1)
• Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34
• Finite- and Infinite-Dimensional Representations of Linear Semisimple Groups
• Compactifications of Symmetric Spaces