This article is cited in 3 papers

Nilpotent action on the KdV variables and 2-dimensional Drinfeld–Sokolov reduction

B. Enriquez


Abstract: 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.

 English version: Theoretical and Mathematical Physics, 1994, 98:3, 256–258

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