Classical N=2 W-superalgebras From Superpseudodifferential Operators

We study the supersymmetric Gelfand-Dickey algebras associated with the 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 as long as the leading order is odd. The decompositions of the coefficient functions into N=1 primary fields are then obtained by covariantizing the superpseudodifferential operators. We discuss the problem of identifying N=2 supermultiplets and work out a couple of supermultiplets by explicit computations.