  We note that a version ``with spectral parameter'' of the Drinfeld-Sokolov
reduction gives a natural mapping from the KdV phase space to the group of
loops with values in $\widehat N_{+}/A, \widehat N_{+}$~: affine nilpotent and
$A$ principal commutative (or anisotropic Cartan) subgroup~; this mapping is
connected to the conserved densities of the hierarchy. We compute the
Feigin-Frenkel action of $\widehat n_{+}$ (defined in terms of screening
operators) on the conserved densities, in the $sl_2$ case.
