Kac-Moody realization of W-algebras

By realizing the W-algebras of Toda field-theories as the algebras of gauge-invariant polynomials of constrained Kac-Moody systems we obtain a simple algorithm for constructing W-algebras without computing the W-generators themselves. In particular this realization yields an identification of a primary field basis for all the W-algebras, quadratic bases for the A, B, C-algebras, and the relation of W-algebras to Casimir algebras. At the quantum level it yields the general formula for the Virasoro centre in terms of the KM level. (orig.)