Asymptotics of G-equivariant Szegő kernels

Rung Tzung Huang; Guokuan Shao

doi:10.1007/s10455-022-09838-0

Asymptotics of G-equivariant Szegő kernels

Rung Tzung Huang, Guokuan Shao

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (X, T^{1 , 0}X) be a compact connected orientable CR manifold of dimension 2 n+ 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.

Original language	English
Pages (from-to)	869-893
Number of pages	25
Journal	Annals of Global Analysis and Geometry
Volume	61
Issue number	4
DOIs	https://doi.org/10.1007/s10455-022-09838-0
State	Published - Jun 2022

Keywords

CR manifold
Equivariant Szegő kernel
Moment map

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10.1007/s10455-022-09838-0

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

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title = "Asymptotics of G-equivariant Szeg{\H o} kernels",

abstract = "Let (X, T1 , 0X) be a compact connected orientable CR manifold of dimension 2 n+ 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{\"o}strand type theorems. When X admits also a transversal CR S1 action, we study the asymptotics of Fourier components of G-equivariant Szeg{\H o} kernels with respect to the S1 action.",

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T1 - Asymptotics of G-equivariant Szegő kernels

AU - Huang, Rung Tzung

AU - Shao, Guokuan

PY - 2022/6

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N2 - Let (X, T1 , 0X) be a compact connected orientable CR manifold of dimension 2 n+ 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.

AB - Let (X, T1 , 0X) be a compact connected orientable CR manifold of dimension 2 n+ 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.

KW - CR manifold

KW - Equivariant Szegő kernel

KW - Moment map

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U2 - 10.1007/s10455-022-09838-0

DO - 10.1007/s10455-022-09838-0

M3 - 期刊論文

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SN - 0232-704X

VL - 61

SP - 869

EP - 893

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 4

ER -

Asymptotics of G-equivariant Szegő kernels

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Keywords

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Analytic Torsion and Geometric Quantization on Complex and Cr Manifolds(2/2)

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