Supergroup OSp(1,4) and classical solutions of the Wess-Zumino model

Superconfirmal transformation properties of the recently constructed O(2,3)-invariant classical solutions of the massless Wess-Zumino model are studied. These properties are shown to be completely determined by two graded subgroups OSp(1,4) of the superconformal group with O(2,3) as the common even subgroup. One of these OSp(1.4) groups is the maximal stability group of the solutions. The other is spontaneously broken down to O(2,3). Its odd transformations generate the explicit Grassmann parameters dependence of the solutions. The results admit the straightforward extension to theories with the Euclidean supersymmetry