CONSTRAINED KP MODELS AS INTEGRABLE MATRIX HIERARCHIES

We formulate the constrained KP hierarchy (denoted by cKP(K+1,M)) as a n affine <(sl)over cap>(M + K + 1) matrix integrable hierarchy general izing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, inc luding the graded structure of the general ized Drinfeld-Sokolov hiera rchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression fo r the second bracket obtained through Dirac reduction of any untwisted affine Kac-Moody current algebra. An explicit example is given for th e case <(sl)over cap>(M + K + 1), for which a closed expression for th e general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple non-r egular element E of sl(Mf K + 1) and the content of the center of the kernel of E. (C) 1997 American Institute of Physics.