Dirac operators and Lie algebra cohomology

DOI10.1090/S1088-4165-06-00267-6zbMath1134.22011arXivmath/0503582WikidataQ115281045 ScholiaQ115281045MaRDI QIDQ5445066

David Renard, Jing-Song Huang, Pavle Pandžić

Publication date: 28 February 2008

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503582

zbMATH Keywords

unitary representationDirac operatorLie algebra cohomologysemisimple Lie groupadmissible representation

Mathematics Subject Classification ID

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

Related Items (17)

Classifying $$A_\mathfrak {q}(\lambda )$$ A q ( λ ) Modules by Their Dirac Cohomology ⋮ Higher Dirac cohomology of modules with generalized infinitesimal character ⋮ Dirac cohomology and geometric quantization ⋮ Dirac cohomology of highest weight modules ⋮ Remarks on the Kostant Dirac operator ⋮ Dirac cohomology for the BGG category \(\mathcal{O} \) ⋮ Jacquet modules and Dirac cohomology ⋮ Dirac cohomology and Dirac induction ⋮ Twisted Dirac Index and Applications to Characters ⋮ A Casselman-Osborne theorem for rational Cherednik algebras ⋮ Dirac series for \(E_{6(-14)}\) ⋮ Dirac index and twisted characters ⋮ Unnamed Item ⋮ Dirac cohomology, elliptic representations and endoscopy ⋮ Dirac cohomology of some Harish-Chandra modules ⋮ Cubic Dirac operators and the strange Freudenthal-de Vries formula for colour Lie algebras ⋮ Dirac Cohomology and Generalization of Classical Branching Rules

Cites Work

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• Representations of real reductive Lie groups
• A generalization of the Bott-Weil theorem and Euler number multiplets of representations
• A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Dirac operator and the discrete series
• Induction functor in noncommutative equivariant cohomology and Dirac cohomology
• Dirac cohomology, unitary representations and a proof of a conjecture of Vogan
• Lie theory and the Chern–Weil homomorphism

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