Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $G$-invariant Szeg\"o kernel asymptotics and CR reduction   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 action $G$. Under certain natural assumptions about
the group action $G$, we show that the $G$-invariant Szeg\"o kernel for $(0,q)$
forms is a complex Fourier integral operator, smoothing away $\mu^{-1}(0)$ and
there is a precise description of the singularity near $\mu^{-1}(0)$, where
$\mu$ 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
$m$-th Fourier component of the $G$-invariant Szeg\"o kernel for $(0,q)$ forms
as $m \to+\infty$. As an application, we show that if $m$ large enough,
quantization commutes with reduction.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas