Non Abelian Asymptotics of Szego Kernels on Compact Quantized Manifolds

Let M be a complex projective manifold with a positive line bundle A on it. The circle bundle X, inside the dual of A, is a contact and CR manifold by positivity of A. The Hardy space H(X) is a closed subspace of L^2(X), the associated projector is called the Szego projector. Let us suppose that a group G acts on M in a Hamiltonian and holomorphic fashion and that the action linearizes to a contact action on X preserving the CR structure. Thus there is an unitary action on H(X); the isotypes are finite dimensional under certain assumptions, so that the corresponding orthogonal projectors have smooth kernels. One is led to study the local asymptotics of the equivariant projectors pertaining to the irreducible representations in a given ray in weight space. In this thesis we consider the case of special unitary group SU(2) and unitary group U(2).