Representations with scalar \(K\)-types and applications

DOI10.1007/BF02776052zbMath1039.22006MaRDI QIDQ1424031

Chen-Bo Zhu

Publication date: 8 March 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

reductive dual pairisotypic component\(K\)-typeinfinitesimal characterHarish-Chandra \((\mathfrak{g}K)\)-modulelocal \(\theta\)-correspondence

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Semisimple Lie groups and their representations (22E46) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items

On holomorphic projection for symplectic groups ⋮ Derived functor modules, dual pairs and \(\mathcal{U}(\mathfrak{g})^K\)-actions ⋮ Transfers of \(K\)-types on local theta lifts of characters and unitary lowest weight modules ⋮ SUR LES PAQUETS D’ARTHUR DE CONTENANT DES MODULES UNITAIRES DE PLUS HAUT POIDS, SCALAIRES ⋮ Phantom holomorphic projections arising from Sturm's formula ⋮ Theta correspondence of automorphic characters

Cites Work

• Unnamed Item
• Singular unitary representations of classical groups
• Degenerate principal series and invariant distributions
• On the local theta-correspondence
• The algebraic structure of the representation of semisimple Lie groups. I
• Invariant distributions of classical groups
• Degenerate principal series and local theta correspondence. II
• One-dimensional representations of \({U(p,q)}\) and the Howe correspondence
• Invariant differential operators on Hermitian symmetric spaces
• Eigendistributions for orthogonal groups and representations of symplectic groups
• Transcending Classical Invariant Theory
• Some Results on Invariant Differential Operators on Symmetric Spaces
• Degenerate principal series and local theta correspondence
• The duality correspondence of infinitesimal characters
• Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces
• Algebraic Results on Representations of Semisimple Lie Groups
• On the Determination of Irreducible Modules by Restriction to a Subalgebra
• Representations of semisimple Lie groups. II