Conformally reduced WZNW theory, new extended chiral algebras and their associated toda type integrable systems

In this paper, the authors propose and analyze a large class of conformal reductions Cons[g(H,d)] of WZNW theory based on the integral gradations of the underlying Lie algebra g. The W bases of the associated W algebras W[g(H,d)] are constructed under the generalized Drinfeld-Sokolov gauge which the authors call O'Raifeartaigh gauge of the constrained Kac-Moody currents, and the equations of motion of the extended Toda type integrable systems corresponding to these W algebras are also derived. As an example, the authors construct explicitly the W algebra associated with the (pqp) block diagonal decomposition of sl2p+q, namely W[(pqp)2], and discuss some of the properties thereof