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arXiv · 2011.09124

Asymptotics of G-equivariant Szeg\H{o} kernels

Rung-Tzung Huang·Guokuan Shao
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Abstract

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 $G$ action. Under certain natural assumptions about the group $G$ action, we define $G$-equivariant Szeg\H{o} kernels and establish the associated Boutet de Monvel-Sj\"ostrand type theorems. When $X$ admits also a transversal CR $S^1$ action, we study the asymptotics of Fourier components of $G$-equivariant Szeg\H{o} kernels with respect to the $S^1$ action.

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Rung-Tzung Huang, Guokuan Shao. 2020-11-14. Asymptotics of G-equivariant Szeg\H{o} kernels. https://arxiv.org/abs/2011.09124

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