Hamiltonian U(2)-actions and Szegö kernel asymptotics

In this paper we shall review some recent results on the asymptotic expansion of the equivariant components of an algebro geometric Szegö kernel determined by the linearization of a Hamiltonian action of U(2) (with certain assumptions). We shall build on the techniques developed in [13], [1], and [11], and therefore ultimately on the microlocal description of the Szegö kernel as a Fourier integral operator in [3]. (paper)