On classifying unitary modules by their Dirac cohomology

DOI10.1007/s11425-017-9097-8zbMath1410.22007OpenAlexW2743091988MaRDI QIDQ724408

Pavle Pandžić, Jing-Song Huang, David A. jun. Vogan

Publication date: 25 July 2018

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-017-9097-8

zbMATH Keywords

Dirac cohomology\((\mathfrak g\),\(K)\)-module\(A_q(\lambda)\) module

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (3)

Classification of \(A_{\mathfrak{q}}(\lambda)\) modules by their Dirac cohomology for type \(D\), \(G_{2}\) and \(\mathfrak{sp}(2 n, \mathbb{R})\) ⋮ Dirac cohomology and character lifting ⋮ On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras

Cites Work

• Dirac cohomology of some Harish-Chandra modules
• Criteria for the unitarizability of some highest weight modules
• Representations of real reductive Lie groups
• A geometric construction of the discrete series for semisimple Lie groups
• Equivalence classes of Vogan diagrams
• Invariants of real forms of affine Kac-Moody Lie algebras
• On the unitary dual of real reductive Lie groups and the \(A_g(\lambda)\) modules: The strongly regular case
• Unitarizability of certain series of representations
• Dirac operator and the discrete series
• Dirac cohomology, unitary representations and a proof of a conjecture of Vogan
• Dirac cohomology, elliptic representations and endoscopy
• Translation principle for Dirac index
• Lie groups beyond an introduction
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