In a series of papers Hanlon conjectured that if L is a semisimple Lie algebra, a Lie algebra of strictly upper triangular matrices, or a Heisenberg Lie algebra, then the homology of a certain extension of L is related to the homology of L in a very natural way. The conjecture for semisimple Lie algebras (known as one of the strong Macdonald conjectures) and for the Lie algebra of strictly upper triangular n \times n matrices where n \ge 4, was settled by Fishel, Grojnowski and Teleman and by Kumar, respectively. Only the case of the Heisenberg Lie algebra remains open. In this talk I will present joint work with Hanlon in which we prove a fundamental part of the conjecture for the 3-dimensional Heisenberg Lie algebra by combinatorial means. Conjectures for other special cases will also be presented.