ASYMPTOTICS OF TORUS EQUIVARIANT SZEGO KERNEL ON A COMPACT CR MANIFOLD

For a compact CR manifold (X, T-1,T-0 X) of dimension 2n + 1, n >= 2, admitting a S-1 x T-d action, if the lattice point (-p1, . . . ,-p(d))( )is an element of Z(d) is a regular value of the associate CR moment map mu, then we establish the asymptotic expansion of the torus equivariant Szego kernel Pi(m,mp1), . . . ,((0))(mpd) (x, y) as m -> +infinity under certain assumptions of the positivity of Levi form and the torus action on Y:= mu(-1)(-p(1), . . . , -p(d)).