  Let G be a reductive group over C. Assume that the Lie algebra g of G has a
given grading (g_j) indexed by a cyclic group Z/m such that g_0 contains a
Cartan subalgebra of g. The subgroup G_0 of G corresponding to g_0 acts on the
variety of nilpotent elements in g_1 with finitely many orbits. We are
interested in computing the local intersection cohomology of the closures of
these orbits with coefficients in irreducible G-equivariant local systems which
are in the "principal block". We show that these can be computed by a purely
combinatorial algorithm.
