AFFINE LIE ALGEBRAIC ORIGIN OF CONSTRAINED KP HIERARCHIES

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approach es, namely linear matrix eigenvalue problem on hermitian symmetric spa ce and constrained KP Lax formulation and it is shown that these appro aches are equivalent. The model is recognized to be the generalized no n-linear Schrodinger (GNLS) hierarchy and it is used as a building blo ck for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Backlund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our con struction uncovers the origin of the Toda lattice structure behind the latter hierarchy. (C) 1995 American Institute of Physics.