Torus equivariant Szeg\H{o} kernel asymptotics on strongly pseudoconvex CR manifolds

TL;DR

This paper investigates the asymptotic behavior of torus equivariant Szeg\

Contribution

It establishes asymptotic expansions for weighted torus equivariant Szeg\

Findings

Asymptotic expansions of Szeg\

Torus symmetry influences kernel behavior

Results applicable to strongly pseudoconvex CR manifolds

Abstract

Let $(X, T^{1,0}X)$ be a compact strongly pseudoconvex CR manifold of dimension $2n+1$. Assume that $X$ admits a Torus action $T^d$. In this work, we study the behavior of torus equivariant Szeg\H{o} kernels and prove that the weighted torus equivariant Szeg\H{o} kernels admit asymptotic expansions.