The hamiltonian reduction of the BRST complex and N=2 SUSY

We study the nonunitary representations of N = 2 Super Virasoro algebra for the rational central charges ĉ < 1. The resolutions for the irreducible representations of N = 2 SV ir in terms of the ”2-d gravity modules” are obtained and their characters are computed. The correspondence between N = 2 nonunitary ”minimal” models and the Virasoro minimal models + 2-d gravity is shown at the level of states. We also define the hamiltonian reduction of the BRST complex of ŝl(N)/ŝl(N) coset to the BRST complex of the W-gravity coupled to the W matter. The case ŝl(2) is considered explicitly. It leads to the presentation of N = 2 Super Virasoro algebra as the Lie algebra cohomology. Finally, we reveal the mechanism of the correspondence ŝl(2)/ŝl(2) coset — 2-d gravity.