Nonstandard Drinfeld-Sokolov reduction

F. Delduc, L. Fehér, L. Gallot

Research output: Contribution to journalArticle

13 Citations (Scopus)


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 the 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 pseudodifferential operators in the Drinfeld-Sokolov framework.

Original languageEnglish
Pages (from-to)5545-5563
Number of pages19
JournalJournal of Physics A: Mathematical and General
Issue number25
Publication statusPublished - Jun 26 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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