Torus equivariant SzegH{o} kernel asymptotics on strongly pseudoconvex CR manifolds

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.