Asymptotics of G-equivariant Szegő kernels

Abstract

Let (X, T 1,0 X) be a compact connected orientable CR manifold of dimension 2n+1 with non-degenerate Levi curvature. Assume that X admits a connected compact Lie group G action. Under certain natural assumptions about the group G action, we define G-equivariant Szegő kernels and establish the associated Boutet de Monvel-Sjöstrand type theorems. When X admits also a transversal CR S 1 action, we study the asymptotics of Fourier components of G-equivariant Szegő kernels with respect to the S 1 action.