A fixed point formula for loop group actions

2000/05/04 by Anton Alekseev, Eckhard Meinrenken, Alekseev, Anton +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.AG #math.DG #math.MP #math.SG

paper · pdf · doi:10.48550/arxiv.math/0005046

28 pages

arxiv created 2000/05/04 · openalex publication_date 2000/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We express the index of the Dirac operator on symplectic quotients of a Hamiltonian loop group manifold with proper moment map in terms of fixed point data.

Citations

• Formulas of Verlinde type for non-simply connected groups
• Symplectic Surgery and the Spinc–Dirac Operator

Related

• Fixed point formula and loop group actions
• A fixed-point formula for Dirac operators on Lie groupoids
• Norm-square localization and the quantization of Hamiltonian loop group spaces
• Quantization of Hamiltonian loop group spaces
• Loops in the Hamiltonian group: a survey