The multiplicities of the equivariant index of twisted Dirac operators

DOI10.1016/j.crma.2014.05.001zbMath1319.53045arXiv1404.2003OpenAlexW2964256232MaRDI QIDQ466176

Michèle Vergne, Paul-Emile Paradan

Publication date: 24 October 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.2003

zbMATH Keywords

index theory\(\mathrm{Spin}^c\) Dirac operatorsgeometric quantisation

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Geometric quantization (53D50)

Related Items (6)

An equivariant index for proper actions. III: The invariant and discrete series indices ⋮ The index theory on non-compact manifolds with proper group action ⋮ A geometric realisation of tempered representations restricted to maximal compact subgroups ⋮ Admissible coadjoint orbits for compact Lie groups ⋮ Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem] ⋮ A geometric formula for multiplicities of 𝐾-types of tempered representations

Cites Work

• Unnamed Item
• Spin-quantization commutes with reduction
• An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg
• Geometric quantization and multiplicities of group representations
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Singular reduction and quantization
• The moment map and line bundles over presymplectic toric manifolds
• Bott towers, complete integrability, and the extended character of representations
• Equivariant index and the moment map for completely integrable torus actions
• Quantization of presymplectic manifolds and circle actions
• Localization of the Riemann-Roch character

This page was built for publication: The multiplicities of the equivariant index of twisted Dirac operators