Reduction of Kac-Moody Systems

The general structure of reductions of the Wess-Zumino-Novikov-Witten theory by first class Kac-Moody constraints is analysed. Algebraic conditions are derived which ensure exact integrability, conformal invariance and TV-symmetry for the reduced effective theories. Solutions to the general algebraic conditions are given leading to new generalized conformal Toda theories. A Lagrangean implementation of the reduction is established in general and is used for setting up the framework for quantizing the effective theories.