Constrained KP Models as Integrable Matrix Hierarchies

H. Aratyn; L. A. Ferreira; J. F. Gomes; A. H. Zimerman

doi:10.1063/1.531908

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arXiv · hep-th/9509096

Constrained KP Models as Integrable Matrix Hierarchies

H. Aratyn·L. A. Ferreira·J. F. Gomes·A. H. Zimerman

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Abstract

We formulate the constrained KP hierarchy (denoted by \cKP$_{K+1,M}$) as an affine ${\widehat {sl}} (M+K+1)$ matrix integrable hierarchy generalizing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized 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 ${\widehat {sl}} (M+K+1)$, 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 {\em non-regular} element $E$ of $sl (M+K+1)$ and the content of the center of the kernel of $E$.

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H. Aratyn, L. A. Ferreira, J. F. Gomes, A. H. Zimerman. 1995-09-15. Constrained KP Models as Integrable Matrix Hierarchies. https://doi.org/10.1063/1.531908

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