The Berkovits method for conformally invariant non-linear σ-models on G/{S⊗U(1)}

We discuss 2-dimmensional non-linear σ-models on the Kähler manifold G/{S⊗U(1)} in the first order formalisim. Using the Berkovits method we explicitly construct the G-symmetry currents and primaries, when G/{S⊗U(1)} is irreducible. It is a variant of the Wakimoto realization of the affine Lie algebra using a particular reducible Kähler manifold G/U(1)r with r the rank of G.