GEOMETRIC QUANTIZATION FOR PROPER MOMENT MAPS

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GEOMETRIC QUANTIZATION FOR PROPER MOMENT MAPS (812)

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by Xiaonan Ma , Weiping Zhang

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12 - 2 self

BibTeX

@MISC{Ma812geometricquantization,
    author = {Xiaonan Ma and Weiping Zhang},
    title = {GEOMETRIC QUANTIZATION FOR PROPER MOMENT MAPS},
    year = {812}
}

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Abstract

Abstract. We establish a geometric quantization formula for Hamiltonian actions of a compact Lie group acting on a non-compact symplectic manifold such that the associated moment map is proper. In particular, we resolve the conjecture of Vergne in this non-compact setting. The famous geometric quantization conjecture of Guillemin and Sternberg [9] states that for a compact pre-quantizable symplectic manifold admitting a Hamiltonian action of a compact Lie group, the principle of “quantization commutes with reduction ” holds. This conjecture was first proved independently by Meinrenken [14] and Vergne [23] for

Keyphrases

geometric quantization proper moment map compact lie group hamiltonian action geometric quantization formula compact pre-quantizable symplectic manifold non-compact setting non-compact symplectic manifold famous geometric quantization conjecture quantization commute associated moment map

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