Z/m-GRADED LIE ALGEBRAS AND PERVERSE SHEAVES, IV

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 go contains a Cartan subalgebra of g. The subgroup G(0) of G corresponding to go acts on the variety of nilpotent elements in g(1) with finitely many orbits. We are interested in computing the local intersection cohomology of closures of these orbits with coefficients in irreducible G(0)-equivariant local systems in the case of the principal block. We show that these can be computed by a purely combinatorial algorithm.