The Dirac operator and the principal series for complex semisimple Lie groups

DOI10.1016/0022-1236(83)90035-6zbMath0542.22013OpenAlexW2149045652MaRDI QIDQ795182

M. G. Penington, Roger Plymen

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0022-1236(83)90035-6

zbMATH Keywords

K-theoryreduced \(C^*\)-algebraconnected complex semisimple Lie groupsConnes-Kasparov conjectureDiract operatorsgeometric construction of discrete series

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25)

Related Items (17)

Parabolic induction and restriction via -algebras and Hilbert -modules ⋮ On the K-Theory of the Reduced $$C^*$$ C ∗ -Algebras of $$GL(n,\mathbb {R})$$ G L ( n , R ) and $$GL(n,\mathbb {C})$$ G L ( n , C ) ⋮ Commutativity of the Haagerup tensor product and base change for operator modules ⋮ On the Connes-Kasparov isomorphism. I: The reduced \(\mathrm{C}^*\)-algebra of a real reductive group and the \(K\)-theory of the tempered dual. ⋮ An equivariant Poincaré duality for proper cocompact actions by matrix groups ⋮ Complex quantum groups and a deformation of the Baum–Connes assembly map ⋮ The Baum–Connes conjecture: an extended survey ⋮ The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras ⋮ Connective \(C^{\ast}\)-algebras ⋮ The ring structure of twisted equivariant \(KK\)-theory for noncompact Lie groups ⋮ Cartan subalgebras in C*-algebras. Existence and uniqueness ⋮ Operator \(K\)-theory and its applications ⋮ On the analogy between real reductive groups and Cartan motion groups: a proof of the Connes-Kasparov isomorphism ⋮ Orbital integrals and \(K\)-theory classes ⋮ Quantisation of presymplectic manifolds, $K$-theory and group representations ⋮ \(K\)-homology and \(K\)-theory of pure braid groups ⋮ Non-commutative differential geometry

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• Restricting Representations of Completely Solvable Lie Groups
• The Plancherel Formula For Complex Semisimple Lie Groups

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