Parafermionic reductions of WZW model

We investigate a class of conformal Non-Abelian-Toda models representing a non compact SL(2,R)/U(1) parafermionions (PF) interacting with a specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras and the exact solution of these models is presented. An important property of this class of models is the affine SL(2 R)q algebra spanned by charges of the chiral and anti chiral currents and the U(1) charge. The classical (Poisson Brackets) algebras of symmetries VGn of these models appears to be of mixed PF-WGn type. They contain together with the local quadratic terms specific for the Wn-algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VAn algebras. The quantum V A2-algebra and its degenerate representations are studied in detail. (author)