On the coefficients of the equivariant Szeg\H{o} kernel asymptotic expansions

TL;DR

This paper computes the lower order coefficients of the equivariant Szeg ext{"o} kernel asymptotic expansion on compact strongly pseudoconvex CR manifolds with group actions, advancing understanding of geometric analysis in this setting.

Contribution

It provides explicit formulas for the first two lower order coefficients of the equivariant Szeg ext{"o} kernel expansion considering $S^1$ and Lie group actions.

Findings

Derived explicit formulas for the coefficients.

Enhanced understanding of Szeg ext{"o} kernel asymptotics.

Applied to CR manifolds with symmetry groups.

Abstract

Let $(X, T^{1,0}X)$ be a compact connected orientable strongly pseudoconvex CR manifold of dimension $2n+1$, $n\geq1$. Assume that $X$ admits a connected compact Lie group $G$ action and a transversal CR $S^1$ action, we compute the coefficients of the first two lower order terms of the equivariant Szeg\H{o} kernel asymptotic expansions with respect to the $S^1$ action.