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科学研究
报告题目:

Asymptotics of torus equivariant Szego kernel on a compact CR manifold

报告人:

Wei-Chuan Shen(Universitat zu K ¨ oln, Mathematisches Institut )

报告时间:

报告地点:

腾讯会议 ID:784 358 067

报告摘要:

The study of the Szego kernel is a classical subject in several complex variables and Cauchy–Riemann geometry. For example, when X is the boundary of a strongly pseudoconvex domain, Boutet de Monvel and Sjostrand proved that locally the Szeg ¨ o kernel ˝ Π(0) (x, y) on (0, 0)-forms is a Fourier integral operator with complex-valued phase function. This kind of description of kernel has profound impact in many aspects, such as spectral theory for Toeplitz operator, geometric quantization and Kahler geometry. ¨ In this talk, we consider a compact CR manifold (X, T 1,0X) of real dimension 2n + 1, n ≥ 2, admitting a S 1 × T d action, d ≥ 1. We consider a lattice point (p1, · · · , pd) ∈ Z d , where (−p1, · · · , −pd) is a regular value of the associate CR moment map µ. Our goal is to study the asymptotic expansion of the corresponding torus equivariant Szego kernel ˝ Π (0) m,mp1,··· ,mpd (x, y) as m → ∞ under certain assumptions on Y := µ −1 (−p1, · · · , −pd). As a corollary, we find a condition when the space of R-equivariant CR functions on an irregular Sasakian manifold is non-trivial in semi-classical limit.