Benoit Dherin, Igor Mencattini
Published 2012-02-04, updated 2012-08-16Version 2
We associate a space of (formal) representations on the space of h-formal power series with coefficients in the space of smooth functions on Rd (which we call quantizations) with an action of a group on Rd by smooth diffeomorphisms. If the action is further volume preserving, these quantizations can be realized as unitary representations on square summable functions on Rd by bounded h-dependent Fourier integral operators, the formal case corresponding to the asymptotics in the limit h going to zero. We construct DGAs controlling these quantizations and prove existence and rigidity results for them.
Comments: 21 pages. We added the notion of formal G-systems, associated with formal quantizations of smooth actions, and proved a corresponding existence and rigidity result
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