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https://hdl.handle.net/2440/61336
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Type: | Journal article |
Title: | Geometric quantization for proper actions |
Author: | Varghese, M. Zhang, W. |
Citation: | Advances in Mathematics, 2010; 225(3):1224-1247 |
Publisher: | Academic Press Inc Elsevier Science |
Issue Date: | 2010 |
ISSN: | 0001-8708 1090-2082 |
Statement of Responsibility: | Varghese Mathai and Weiping Zhang |
Abstract: | We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the case of proper cocompact actions. Our invariant index is used to show that an analog of the Guillemin-Sternberg geometric quantization conjecture holds if M is symplectic with a Hamiltonian action of G that is proper and cocompact. This essentially solves a conjecture of Hochs and Landsman. © 2010 Elsevier Inc. |
Keywords: | Geometric quantization Locally compact groups Hochs–Landsman conjecture Guillemin–Sternberg conjecture Equivariant K-theory Index theorem for generalized orbifolds |
Rights: | Copyright 2010 Elsevier Inc. All rights reserved. |
DOI: | 10.1016/j.aim.2010.03.023 |
Grant ID: | ARC |
Published version: | http://dx.doi.org/10.1016/j.aim.2010.03.023 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
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