  Suppose that the compact and connected Lie group G acts holomorphically on
the irreducible complex projective manifold M, and that the action linearizes
to the Hermitian ample line bundle L on M. Assume that 0 is a regular value of
the associated moment map. The spaces of global holomorphic sections of powers
of L may be decomposed over the finite dimensional irreducible representations
of G. In this paper, we study how the holomorphic sections in each equivariant
piece asymptotically concentrate along the zero locus of the moment map. In the
special case where G acts freely on the zero locus of the moment map, this
relates the scaling limits of the Szego kernel of the quotient to the scaling
limits of the invariant part of the Szego kernel of (M,L).
