A K-theoretic note on geometric quantization |
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Authors: | David S Metzler |
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Institution: | (1) Department of Mathematics, Rice University, 6100 S. Main Street, Houston, TX 77005-1892, USA. e-mail: metzler@math.rice.edu, US |
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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.
Received: 9 March 1999 |
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Keywords: | Mathematics Subject Classification (1991):58F/19L |
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