Nonstandard Drinfeld-Sokolov reduction

Delduc, F., Fehér, L. and Gallot, L. (1997) Nonstandard Drinfeld-Sokolov reduction. (Preprint)

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Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (A, Λ, d_1, d_0 ), where the d_i are Z-gradations of a loop algebra A and Λ ϵ A is a semisimple element of nonzero d_1-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the d_1-grade zero part of A into a vector space direct sum of two subalgebras. This permits one to interpret certain Gelfand-Dickey type systems associated with nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:07
Last Modified: 20 Dec 2022 09:05

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