Asymptotics of G-equivariant Szegő kernels

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

26 pages. arXiv admin note: substantial text overlap with arXiv:1702.05012, arXiv:2009.10529

References in corpus (1)

• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles