Wednesday, September 5, 2012

1209.0059 (Roberto Paoletti)

Lower order asymptotics for Szegö and Toeplitz kernels under
Hamiltonian circle actions

Roberto Paoletti
We consider a natural variant of Berezin-Toeplitz quantization of compact K\"{a}hler manifolds, in the presence of a Hamiltonian circle action lifting to the quantizing line bundle. Assuming that the moment map is positive, we study the diagonal asymptotics of the associated Szeg\"{o} and Toeplitz operators, and specifically their relation to the moment map and to the geometry of a certain symplectic quotient. When the underlying action is trivial and the moment map is taken to be identically equal to one, this scheme coincides with the usual Berezin-Toeplitz quantization. This continues previous work on near-diagonal scaling asymptotics of equivariant Szeg\"{o} kernels in the presence of Hamiltonian torus actions.
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