NILPOTENT ACTION ON THE KDV VARIABLES AND 2-DIMENSIONAL DRINFELD-SOKOLOV REDUCTION

We note that a version ''with spectral parameter'' of the Drinfeld-Sok olov reduction gives a natural mapping from the KdV phase space to the group of loops with values in (N) over cap(+)/A,(N) over cap(+) : aff ine nilpotent and A principal commutative (or anisotropic Cartan) subg roup; this mapping is connected to the conserved densities of the hier archy. We compute the Feigin-Frenkel action of (n) over cap(+) (define d in terms of screening operators) on the conserved densities in the s /(2) case.