Existence of natural and projectively equivariant quantizations |
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Authors: | Sarah Hansoul |
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Institution: | Department of Mathematics, University of Liège, Grande Traverse, 12, B-4000 Liège, Belgium |
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Abstract: | We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operators, and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values. |
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Keywords: | 58A05 53B05 46L65 58J70 |
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