JournalsggdVol. 16, No. 4pp. 1369–1387

Asymptotic representations of Hamiltonian diffeomorphisms and quantization

  • Laurent Charles

    Université de Paris, CNRS, France; Sorbonne Université, Paris

  • Leonid Polterovich

    Tel Aviv University, Israel
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Abstract

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.

Cite this article

Laurent Charles, Leonid Polterovich, Asymptotic representations of Hamiltonian diffeomorphisms and quantization. Groups Geom. Dyn. 16 (2022), no. 4, pp. 1369–1387

DOI 10.4171/GGD/696