Symplectic reduction and a weighted multiplicity formula for twisted \(\text{Spin}^c\)-Dirac operators (Q1299463)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symplectic reduction and a weighted multiplicity formula for twisted \(\text{Spin}^c\)-Dirac operators |
scientific article |
Statements
Symplectic reduction and a weighted multiplicity formula for twisted \(\text{Spin}^c\)-Dirac operators (English)
0 references
1 January 2001
0 references
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.
0 references
symplectic reduction
0 references
twisted Spin\(^c\) Dirac operator
0 references
symplectic manifold
0 references
\(G\)-equivariant Hermitian vector bundle
0 references
weighted multiplicity formula
0 references
