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An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg

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Inventiones mathematicae Aims and scope

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.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York, NY 10012, USA (e-mail: ytian@cims.nyu.edu), , , , , , US

    Youliang Tian

  2. Nankai Institute of Mathematics, Tianjin 300071, People's Republic of China (e-mail: weiping@sun.nankai.edu.cn), , , , , , CN

    Weiping Zhang

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  1. Youliang Tian
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  2. Weiping Zhang
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Oblatum 3-IX-1996 & 4-VIII-1997

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Tian, Y., Zhang, W. An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg. Invent math 132, 229–259 (1998). https://doi.org/10.1007/s002220050223

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  • DOI: https://doi.org/10.1007/s002220050223

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