Szeg\"{o} kernel equivariant asymptotics under Hamiltonian Lie group actions
Symplectic Geometry
2021-04-06 v1 Complex Variables
Abstract
Suppose that a compact and connected Lie group acts on a complex Hodge manifold in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle on . Then there is an induced unitary representation on the associated Hardy space and, if the moment map of the action is nowhere vanishing, the corresponding isotypical components are all finite dimensional. We study the asymptotic concentration behavior of the corresponding equivariant Szeg\"{o} kernels near certain loci defined by the moment map.
Cite
@article{arxiv.2104.01801,
title = {Szeg\"{o} kernel equivariant asymptotics under Hamiltonian Lie group actions},
author = {Roberto Paoletti},
journal= {arXiv preprint arXiv:2104.01801},
year = {2021}
}