CLASSICAL N=2 W-SUPERALGEBRAS FROM SUPERPSEUDODIFFERENTIAL OPERATORS

Abstract

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 when 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.