Equivariant indices of \(\operatorname{Spin}^c\)-Dirac operators for proper moment maps

DOI10.1215/00127094-3792923zbMath1370.58010arXiv1503.00801OpenAlexW3099415605MaRDI QIDQ2627838

Peter Hochs, Yanli Song

Publication date: 1 June 2017

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00801

zbMATH Keywords

moment mapindex theoryproper group action\({\operatorname{Spin}}^{c}\)-Dirac operator

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Momentum maps; symplectic reduction (53D20)

Related Items (12)

Quantization commutes with reduction, a survey ⋮ Geometric quantization on CR manifolds ⋮ Quantization of Hamiltonian loop group spaces ⋮ A geometric realisation of tempered representations restricted to maximal compact subgroups ⋮ A \(KK\)-theoretic perspective on deformed Dirac operators ⋮ A fixed point theorem on noncompact manifolds ⋮ On the Vergne conjecture ⋮ Formal geometric quantization. III: Functoriality in the \(\mathrm{spin}^c\) setting ⋮ Kirillov's orbit method: the case of discrete series representations ⋮ Quantization commutes with singular reduction: Cotangent bundles of compact Lie groups ⋮ Norm-square localization and the quantization of Hamiltonian loop group spaces ⋮ A geometric formula for multiplicities of 𝐾-types of tempered representations

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