Constrained KP models as integrable matrix hierarchies

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