NONPOLYNOMIAL REALIZATIONS OF W-ALGEBRAS

Relaxing first-class constraint conditions in the usual Drinfeld-Sokol ov Hamiltonian reduction leads, after symmetry fixing, to realizations of W algebras expressed in terms of all the J current components. Gen eral results are given for G a nonexceptional simple (finite and affin e) algebra. Such calculations directly provide the commutant, in the ( closure of) G enveloping algebra, of the nilpotent subalgebra G_, wher e the subscript refers to the chosen gradation in G. In the affine cas e, explicit expressions are presented for the Virasoro, W3, and Bersha dsky algebras at the quantum level.