Nonstandard Drinfeld-Sokolov reduction
نویسنده
چکیده
Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (A,Λ, d1, d0), where the di are Z-gradations of a loop algebra A and Λ ∈ A is a semisimple element of nonzero d1-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 d1-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 a nonstandard splitting of the algebra of pseudo-differential operators in the Drinfeld-Sokolov framework. ∗ Permanent address: Department of Theoretical Physics, József Attila University, H-6720 Szeged, Hungary. ENSLAPP, URA 14-36 du CNRS, associé à l’E.N.S. de Lyon et au L.A.P.P.
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