Abstract:

Let X be a compact connected strongly pseudoconvex CR manifold. Assume that X admits a connected compact Lie group G action. Under certain natural assumptions on G, we show that the G-equivariant Szego kernel is a complex Fourier integral operator, smoothing away from μ⁻¹(0), where μ denotes the CR moment map. By applying our result to the case when X also admits a transversal CR S¹ action, we deduce an asymptotic expansion for the m-th Fourier component of the G-equivariant Szego kernel as m→∞ and compute the coefficients of the first two lower order terms. This talk is based on joint work with Chin-Yu Hsiao and Rung-Tzung Huang.