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Nilpotent action on the KdV variables and 2-dimensional Drinfeld-Sokolov reduction. (English) Zbl 0833.35123
Theor. Math. Phys. 98, No. 3, 256-258 (1994) and Teor. Mat. Fiz. 98, No. 3, 375-378 (1994).
Summary: 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 \(\widehat N_+/A\), with \(\widehat N_+\) affine nilpotent and \(A\) the 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 \(\text{sl}_2\) case.

35Q53 KdV equations (Korteweg-de Vries equations)
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
Full Text: DOI arXiv
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