Symplectic reduction and a weighted multiplicity formula for twisted $\mathrm{Spin}^c$-Dirac operators
Copyright policy )Symplectic reduction and a weighted multiplicity formula for twisted $\mathrm{Spin}^c$-Dirac operators
In this paper the authors extend the analytic approach to the Guillemin-Sternberg conjecture developed in their paper [Invent. Math. 132, 229-259 (1998; Zbl 0944.53047)] to the cases where the \(\text{Spin}^c\)-complex under consideration is twisted by certain exterior power bundles of the cotangent bundle. The authors obtain a weighted quantization formula in the presence of commuting Hamiltonian actions.
Geometric quantization, symplectic manifold, weighted multiplicity formula, twisted Spin\(^c\) Dirac operator, Spin and Spin\({}^c\) geometry, symplectic reduction, Geometry and quantization, symplectic methods, \(G\)-equivariant Hermitian vector bundle
Geometric quantization, symplectic manifold, weighted multiplicity formula, twisted Spin\(^c\) Dirac operator, Spin and Spin\({}^c\) geometry, symplectic reduction, Geometry and quantization, symplectic methods, \(G\)-equivariant Hermitian vector bundle
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