Graded Parafermions

A graded generalization of the Z_k parafermionic current osp(1|2)/U(1) coset conformal field theory. The structure of the parafermionic highest-weight modules is analyzed and the dimensions of the fields of the theory are determined. A free field realization of the graded parafermionic system is obtained and the structure constants of the current algebra are found. Although the theory is not unitary, it presents good reducibility properties.Comment: 27 pages, LaTeX, 1 eps file. Typos correcte

On Two-Current Realization of KP Hierarchy

A simple description of the KP hierarchy and its multi-hamiltonian structure is given in terms of two Bose currents. A deformation scheme connecting various W-infinity algebras and relation between two fundamental nonlinear structures are discussed. Properties of Fa\'a di Bruno polynomials are extensively explored in this construction. Applications of our method are given for the Conformal Affine Toda model, WZNW models and discrete KP approach to Toda lattice chain.Comment: 28 pages, IFT-P/020/92-SAO-PAULO, Late