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The Koszul complex of a moment map. (English) Zbl 1286.53082

As the authors explain in their introduction, the main inspiration for this paper comes from the Batalin-Fradkin-Vilkovisky (BFV) approach relating the symplectic reduction of constrained systems and their quantization. In technical terms the BFV method is based on the Koszul complex \(\mathcal{K}(J,C^\infty (V))\) of the moment map. Actually the main result of the paper can be formulated as the statement that the Koszul complex is a resolution of the smooth functions on the zero level set \( Z=J^{-1}(0) \) of the momentum mapping \(J\) if and only if the complexification of each symplectic slice representation at the points of \(Z\) is 1-large.

MSC:

53D20 Momentum maps; symplectic reduction
53D05 Symplectic manifolds (general theory)
53D50 Geometric quantization
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