Abstract:
We give a purely K-theoretic proof of a case of the “quantization commutes with reduction” result, conjectured by Guillemin and Sternberg and proved by Meinrenken and Vergne. We show that the quantization is simply a pushforward in K-theory, and use Lerman's symplectic cutting and the localization theorem in equivariant K-theory to prove that quantization commutes with reduction. The case where G=S 1 and the action is free on the zero level set of the moment map is addressed.
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Received: 9 March 1999
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Metzler, D. A K-theoretic note on geometric quantization. manuscripta math. 100, 277–289 (1999). https://doi.org/10.1007/s002290050200
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DOI: https://doi.org/10.1007/s002290050200