An analytic proof of the geometric quantization conjecture

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An analytic proof of the geometric quantization conjecture (1998)

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by Youliang Tian , Weiping Zhang

Venue:	of GuilleminSternberg, Invent. Math 132
Citations:	55 - 8 self

BibTeX

@INPROCEEDINGS{Tian98ananalytic,
    author = {Youliang Tian and Weiping Zhang},
    title = {An analytic proof of the geometric quantization conjecture},
    booktitle = {of GuilleminSternberg, Invent. Math 132},
    year = {1998},
    pages = {229--259}
}

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Abstract

Abstract. We present a direct analytic approach to the Guillemin-Sternberg conjecture [GS] that ‘geometric quantization commutes with symplectic reduction’, which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods also lead immediately to further extensions in various contexts. Let M;x be a closed symplectic manifold such that there is a Hermitian line bundle L over M admitting a Hermitian connection rL with the prop-erty that ÿ1p

Keyphrases

geometric quantization conjecture analytic proof geometric quantization commute hermitian line bundle guillemin-sternberg conjecture g vergne v1 meinrenken m1 direct analytic approach new proof various context hermitian connection rl symplectic reduction closed symplectic manifold

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