ar X iv : h ep - t h / 97 12 10 2 v 1 9 D ec 1 99 7 hep - th / 9712102

We classify and explicitly construct the embedding diagrams of Verma modules over the N =2 supersymmetric extension of the Virasoro algebra. The essential ingredient of the solution consists in drawing the distinction between two different types of submodules appearing in N = 2 Verma modules. The problem is simplified by associating to every N=2 Verma module a relaxed Verma module over the affine algebra ŝl(2) with an isomorphic embedding diagram. We then make use of the mechanism according to which the structure of the N=2/relaxedŝl(2) embedding diagrams can be found knowing the standard embedding diagrams of ŝl(2) Verma modules. The resulting classification of the N = 2/relaxed-ŝl(2) embedding diagrams follows the I-II-III pattern extended by an additional indication of the number (0, 1, or 2) and the twists of the standard ŝl(2) embedding diagrams contained in a given N=2/relaxed-ŝl(2) embedding diagram.