W-GEOMETRY OF THE TODA SYSTEMS ASSOCIATED WITH NON-EXCEPTIONAL SIMPLELIE-ALGEBRAS

The present paper describes the W-geometry of the Abelian finite non-p eriodic (conformal) Toda systems associated with the B, C and D series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Plucker embed ding of the A-case to the flag manifolds associated with the fundament al representations of B-n, C-n and D-n, and a direct proof that the co rresponding Kahler potentials satisfy the system of two-dimensional fi nite non-periodic (conformal) Toda equations. It is shown that the W-g eometry of the type mentioned above coincide with the differential geo metry of special holomorphic (W) surfaces in target spaces which are s ubmanifolds (quadrics) of CPN with appropriate choices of N. In additi on, these W-surfaces are de fined to satisfy quadratic holomorphic dif ferential conditions that ensure consistency of the generalized Plucke r embedding. These conditions are automatically fulfilled when Toda eq uations hold.