Toeplitz operators and Hamiltonian torus action
| dc.creator | Charles, L. | |
| dc.date | 2004-05-07 | |
| dc.date | 2006-02-02 | |
| dc.date.accessioned | 2026-07-07T06:36:45Z | |
| dc.date.available | 2026-07-07T06:36:45Z | |
| dc.description | 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. | |
| dc.description | corrected typos, accepted for publication in J. Funct. Anal | |
| dc.identifier | https://arxiv.org/abs/math/0405128 | |
| dc.identifier | http://arxiv.org/abs/math/0405128 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100190 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 53D20; 53D50; 81S30; 47L80; 37P20 | |
| dc.title | Toeplitz operators and Hamiltonian torus action | |
| dc.type | text |