The classification of quasi primary fields is outlined. It is proved that the only conserved quasi primary currents are the energy momentum tensor and the O(N)Noether currents. Derivation of all quasi primary fields and the resolution of degeneracy is sketched. Finally the limits d = 2 and d = 4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so. (T...

We clarify the notion of the DS — generalized Drinfeld-Sokolov — reduction approach to classical W-algebras. We first strengthen an earlier theorem which showed that an sl(2) embedding S ⊂ G can be associated to every DS reduction. We then use the fact that a W-algebra must have a quasi-primary basis to derive severe restrictions on the possible reductions corresponding to a given sl(2) embeddi...