Geodesic
Asymptotic representations of Hamiltonian diffeomorphisms and quantization
Laurent Charles1 ; Leonid Polterovich2 orcid
1Université de Paris, CNRS, France; Sorbonne Université, Paris
2Tel Aviv University, Israel
Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1369-1387

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DOI

We show that for a special class of geometric quantizations with “small” quantum errors, the quantum classical correspondence gives rise to an asymptotic projective unitary representation of the group of Hamiltonian diffeomorphisms. As an application, we get an obstruction to Hamiltonian actions of finitely presented groups.
DOI : 10.4171/ggd/696
Classification : 53-XX, 37-XX, 81-XX
Mots-clés : Symplectic manifold, Hamiltonian diffeomorphism, Berezin–Toeplitz quantization, asymptotic representation

Laurent Charles  1   ; Leonid Polterovich  2

1 Université de Paris, CNRS, France; Sorbonne Université, Paris
2 Tel Aviv University, Israel 
Laurent Charles; Leonid Polterovich. Asymptotic representations of Hamiltonian diffeomorphisms and quantization. Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1369-1387. doi: 10.4171/ggd/696
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     title = {Asymptotic representations of {Hamiltonian} diffeomorphisms and quantization},
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     year = {2022},
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     number = {4},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/696/}
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