  We describe the moduli space of SU(N) instantons in the presence of a general
surface operator of type N=n_1+ ... +n_M in terms of the representations of the
so-called chain-saw quiver, which allows us to write down the instanton
partition function as a summation over the fixed point contributions labeled by
Young diagrams. We find that the instanton partition function depends on the
ordering of n_I which fixes a choice of the parabolic structure. This is in
accord with the fact that the Verma module of the W-algebra also depends on the
ordering of n_I. By explicit calculations, we check that the partition function
agrees with the norm of a coherent state in the corresponding Verma module.
