The bihamiltonian structure of the Drinfel'd-Sokolov hierarchies related to the affine twisted lie algebras

Paolo Casati


Abstract. This paper presents a bihamiltonian construction of the Drinfel'd--Sokolov hierarchies corresponding to the twisted affine Lie algebras. We show, indeed, that these hierarchies can be framed in the general theory of bihamiltonian manifolds, by applying an extended bihamiltonian reduction theorem stated and proved in the paper.

AMSclassification. 58F, 17B67

Keywords. Bihamiltonian manifolds, twisted affine Kac--Moody algebras