R617, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 617室)

G-equivariant Szegő Kernel Asymptotics on CR Manifolds

Guokuan Shao (Sun Yat-Sen University)

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 S^{1} 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.