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Abstract
Let (X, T^{1 , 0}X) be a compact connected orientable CR manifold of dimension 2 n+ 1 with nondegenerate Levi curvature. Assume that X admits a connected compact Lie group G action. Under certain natural assumptions about the group G action, we show that the Ginvariant Szegő kernel for (0, q) forms is a complex Fourier integral operator, smoothing away μ^{ 1}(0) and there is a precise description of the singularity near μ^{ 1}(0) , where μ denotes the CR moment map. We apply our result to the case when X admits a transversal CR S^{1} action and deduce an asymptotic expansion for the mth Fourier component of the Ginvariant Szegő kernel for (0, q) forms as m→ + ∞ and when q= 0 , we recover Xiaonan Ma and Weiping Zhang’s result about the existence of the Ginvariant Bergman kernel for ample line bundles. As an application, we show that if m large enough, quantization commutes with reduction.
Original language  English 

Article number  47 
Journal  Calculus of Variations and Partial Differential Equations 
Volume  60 
Issue number  1 
DOIs  
State  Published  Feb 2021 
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Dive into the research topics of 'Ginvariant Szegő kernel asymptotics and CR reduction'. Together they form a unique fingerprint.Projects
 2 Finished

Analytic Torsion and Geometric Quantization on Complex and Cr Manifolds(2/2)
Huang, R.T. (PI)
1/08/19 → 31/07/21
Project: Research

A Study on Some Geometric Invariants on Manifolds(2/2)
Huang, R.T. (PI)
1/08/17 → 31/07/18
Project: Research