Geodesic
Nilpotent action on the KdV variables and 2-dimensional Drinfeld--Sokolov reduction
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 375-378

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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. 
@article{TMF_1994_98_3_a6,
     author = {B. Enriquez},
     title = {Nilpotent action on the {KdV} variables and 2-dimensional {Drinfeld--Sokolov} reduction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {375--378},
     publisher = {mathdoc},
     volume = {98},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a6/}
}
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B. Enriquez. Nilpotent action on the KdV variables and 2-dimensional Drinfeld--Sokolov reduction. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 375-378. http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a6/