Z/m-graded Lie algebras and perverse sheaves, IV

© 2020 American Mathematical Society. Let G be a reductive group over C. Assume that the Lie algebra g of G has a given grading (gj ) indexed by a cyclic group Z/m such that g0 contains a Cartan subalgebra of g. The subgroup G0 of G corresponding to g0 acts on the variety of nilpotent elements in g1 with finitely many orbits. We are interested in computing the local intersection cohomology of closures of these orbits with coefficients in irreducible G0-equivariant local systems in the case of the principal block. We show that these can be computed by a purely combinatorial algorithm.