Parabolic induction and restriction via -algebras and Hilbert -modules

DOI10.1112/S0010437X15007824zbMath1346.22005arXiv1409.8654MaRDI QIDQ3186429

Pierre Clare, Nigel Higson, Tyrone Crisp

Publication date: 9 August 2016

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.8654

zbMATH Keywords

Hilbert \(C^*\)-moduletempered representationparabolic subgroupreal reductive groupreduced group \(C^*\)-algebra

Mathematics Subject Classification ID

(C^*)-modules (46L08) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (18)

An index theorem for higher orbital integrals ⋮ Frobenius C∗-algebras and local adjunctions of C∗-correspondences ⋮ Continuity of the Mackey-Higson bijection ⋮ Frobenius reciprocity and the Haagerup tensor product ⋮ Commutativity of the Haagerup tensor product and base change for operator modules ⋮ On a spectral theorem of Weyl ⋮ On the Connes-Kasparov isomorphism. I: The reduced \(\mathrm{C}^*\)-algebra of a real reductive group and the \(K\)-theory of the tempered dual. ⋮ ADJOINT FUNCTORS BETWEEN CATEGORIES OF HILBERT -MODULES ⋮ A second adjoint theorem for \SL(2,ℝ) ⋮ The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras ⋮ Connective \(C^{\ast}\)-algebras ⋮ Descent of Hilbert \(C^*\)-modules ⋮ The ring structure of twisted equivariant \(KK\)-theory for noncompact Lie groups ⋮ C*-algebraic normalization and Godement-Jacquet factors ⋮ On the analogy between real reductive groups and Cartan motion groups: a proof of the Connes-Kasparov isomorphism ⋮ Orbital integrals and \(K\)-theory classes ⋮ Explicit Rieffel induction module for quantum groups ⋮ Graded hypoellipticity of BGG sequences

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