Abstract
We show how the moduli space of flatSU(2) connections on a two-manifold can be quantized in the real polarization of [15], using the methods of [6]. The dimension of the quantization, given by the number of integral fibres of the polarization, matches the Verlinde formula, which is known to give the dimension of the quantization of this space in a Kähler polarization.
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Communicated by A. Jaffe
Supported in part by MSRI under NSF Grant 85-05550
Supported in part by an NSF Graduate fellowship, and by a grant-in-aid from the J. Seward Johnson Charitable Trust
Supported in part by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291. Address as of January 1, 1993: Department of Mathematics, Columbia University, New York, NY 10027, USA
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Jeffrey, L.C., Weitsman, J. Bohr-sommerfeld orbits in the moduli space of flat connections and the Verlinde dimension formula. Commun.Math. Phys. 150, 593–630 (1992). https://doi.org/10.1007/BF02096964
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DOI: https://doi.org/10.1007/BF02096964