Norm-square localization and the quantization of Hamiltonian loop group spaces

DOI10.1016/j.jfa.2019.108445zbMath1433.58021arXiv1810.02347OpenAlexW2996921510WikidataQ126457004 ScholiaQ126457004MaRDI QIDQ2295695

Yanyan Li

Publication date: 14 February 2020

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

Full work available at URL: https://arxiv.org/abs/1810.02347

zbMATH Keywords

symplectic geometryDirac operatorsquantizationloop groups

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Momentum maps; symplectic reduction (53D20) Boundary value problems on manifolds (58J32) Geometric quantization (53D50)

Related Items (4)

Geometric \(K\)-homology and the Freed-Hopkins-Teleman theorem ⋮ Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds ⋮ A \(KK\)-theoretic perspective on deformed Dirac operators ⋮ Towards a quantization of the double via the enhanced symplectic ``category

Cites Work

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• Localization for equivariant cohomology with varying polarization
• A local global principle for regular operators in Hilbert \(C^*\)-modules
• Norm-square localization for Hamiltonian \(L G\)-spaces
• Formal geometric quantization. II
• Splitting of the family index
• Geometric quantization for proper moment maps
• Equivariant KK-theory and the Novikov conjecture
• An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg
• Continuity and analyticity of families of self-adjoint Dirac operators on a manifold with boundary
• Geometric quantization and multiplicities of group representations
• Symplectic surgery and the Spin\(^c\)-Dirac operator
• Lie group valued moment maps
• Singular reduction and quantization
• On the index of geometrical operators for Riemannian manifolds with boundary
• \([Q,R=0\) and Kostant partition functions]
• Equivariant Dirac operators and differentiable geometric invariant theory
• Hamiltonian loop group actions and Verlinde factorization
• Index theorem for equivariant Dirac operators on noncompact manifolds
• The Verlinde formulas as fixed point formulas.
• Surjectivity for Hamiltonian loop group spaces
• The equivariant index of transversally elliptic operators
• Geometric quantization for proper moment maps: the Vergne conjecture
• Geometric \(K\)-homology and the Freed-Hopkins-Teleman theorem
• Spinor modules for Hamiltonian loop group spaces
• Quantization of Hamiltonian loop group spaces
• Equivariant indices of \(\operatorname{Spin}^c\)-Dirac operators for proper moment maps
• The decomposition formula for Verlinde sums
• A short proof of an index theorem
• Transversal Index and L2-index for Manifolds with Boundary
• Index of transversally elliptic operators
• Spectral asymmetry and Riemannian Geometry. I
• Twisted K-Homology and Group-Valued Moment Maps
• Loop groups and twisted $K$-theory II
• Witten Non Abelian Localization for Equivariant K-Theory, and the [𝑄,𝑅=0 Theorem]
• Lectures on group-valued moment maps and Verlinde formulas
• Guide to Elliptic Boundary Value Problems for Dirac-Type Operators
• Boundary Value Problems for Elliptic Differential Operators of First Order
• Localization of the Riemann-Roch character

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