Wakimoto realizations of current and exchange algebras

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies $K{b}^{\mathrm{\prime }}=Jb$. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.