Hamiltonian Reduction of 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 SVir 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 (q,p) minimal models coupled to 2-d gravity is shown at the level of states. We also define the Hamiltonian reduction of the BRST complex of \(\widehat{sl}\left( N \right)/\widehat{sl}\left( N \right)\) coset to the BRST complex of the W-gravity coupled to the W matter. The case \( \widehat{{sl}}\left( 2 \right) \) is considered explicitly. Finally, we trace down the mechanism of the correspondence between \( \widehat{{sl}}\left( 2 \right)/\widehat{{sl}}\left( 2 \right) \) coset and 2-d gravity models.