On the coefficients of the equivariant Szegő kernel asymptotic expansions

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 Szegő kernel asymptotic expansions with respect to the $S^1$ action.

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