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Article Dans Une Revue Journal of Functional Analysis Année : 2006

Toeplitz operators and Hamiltonian torus action

Résumé

This paper is devoted to semi-classical aspects of symplectic reduction. Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus action. Guillemin and Sternberg introduced an isomorphism between the invariant part of the quantum space associated to M and the quantum space associated to the symplectic quotient of M, provided this quotient is non-singular. We prove that this isomorphism is a Fourier integral operator and that the Toeplitz operators of M descend to Toeplitz operators of the reduced phase space. We also extend these results to the case where the symplectic quotient is an orbifold and estimate the spectral density of a reduced Toeplitz operator, a result related to the Riemann-Roch-Kawazaki theorem.

Dates et versions

hal-00137379 , version 1 (19-03-2007)

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Citer

L. Charles. Toeplitz operators and Hamiltonian torus action. Journal of Functional Analysis, 2006, 236 numéro 1, pp.299-350. ⟨hal-00137379⟩
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