Szegö kernel equivariant asymptotics under Hamiltonian Lie group actions

Suppose that a compact and connected Lie group G acts on complex Hodge manifold M in holomorphic Hamiltonian manner, the action linearizes to positive line bundle A M. Then there is an induced unitary representation associated Hardy space and, if moment map of nowhere vanishing, corresponding isotypical components are all finite dimensional. We study asymptotic concentration behavior equivariant Szegö kernels near certain loci defined by map.