Equivariant Asymptotics of Szegő kernels under Hamiltonian SU(2)-actions

Let M be complex projective manifold, and A a positive line bundle on it. Assume that G = SU(2) acts on M in a Hamiltonian manner, with nowhere vanishing moment map, and that this action linearizes to A. Then there is an associated unitary representation of G on the associated algebro-geometric Hardy space, and the isotypical components are all finite dimensional. We consider the local and global asymptotic properties of the equivariant projector associated to a weight k ν, when ν is fixed and k → +∞.