For a finite-dimensional reductive Lie algebra g, we will introduce and study a derived representation scheme
DRep(A,g) parametrizing the representations of a given Lie algebra A in g. We relate the homology
of DRep(A,g) to the classical (Chevalley-Eilenberg) cohomology of current Lie algebras. This
allows us to construct a canonical map F from DRep(A,g)^G to DRep(A,h)^W, relating the G-invariant part of representation homology of A in g to the W-invariant part of representation homology of A in a
Cartan subalgebra of g. We call this map the derived Harish-Chandra homomorphism as it is a natural homological extension of the classical Harish-Chandra restriction map. We conjecture that if A is a two dimensional abelian Lie algebra, then F is a quasi-isomorphism for any finite-dimensional reductive Lie algebra g. We provide some evidence
for this conjecture and explain the relation to the strong Macdonald conjectures proposed by P.Hanlon and B.Feigin
in the late 80s and recently proved (in full generality) by S. Fishel, I. Grojnowski and C. Teleman.

(Joint work with Yu. Berest, G. Felder, S. Patotski and T. Willwacher)