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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. G. Drinfeld, V. V. Sokolov, Jour. Sov. Math., 30 (1985), 1975–2036 | DOI | Zbl

[2] B. Feigin, E. Frenkel, “Integrals of motions and quantum groups”, Integrable systems and quantum groups (Montecatini Terme, 1993), Lecture Notes in Math., 1620, Springer, Berlin, 1996, 349–418 | DOI | MR | Zbl

[3] L. A. Dickey, Soliton Equations and Hamiltonian Systems, Advanced Series in Mathematical Physics, 12, World Scient., 1991 | DOI | MR | Zbl