Asymptotics of G-equivariant Szegő kernels

2020/11/14 by Rung-Tzung Huang, Huang, Rung-Tzung, Guokuan Shao +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2011.09124

openalex publication_date 2020/11/14 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

Let (X, T^1,0X) 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 Szegő kernels and establish the associated Boutet de Monvel-Sjöstrand type theorems. When X admits also a transversal CR S¹ action, we study the asymptotics of Fourier components of G-equivariant Szegő kernels with respect to the S¹ action.

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