The Berkovits Method for Conformally Invariant Non-linear Sigma-models on G/H

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