CLASSICAL N=2 W-SUPERALGEBRAS FROM SUPERPSEUDODIFFERENTIAL OPERATORS

We study the supersymmetric Gelfand-Dickey algebras associated with th e superpseudodifferential operators of positive, as well as negative, leading order. We show that, upon the usual constraint, these algebras contain the N = 2 super Virasoro algebra as a subalgebra when the lea ding order is odd. The decompositions of the coefficient functions int o N = 1 primary fields are then obtained by covariantizing the superps eudodifferential operators. We discuss the problem of identifying N = 2 supermultiplets and work out a couple of supermultiplets by explicit computations.