Algebraic aspects of the discrete KP hierarchy Original Research Article

We discuss some algebraic properties of the so-called discrete KP hierarchy, an integrable system defined on a space of infinite matrices. We give an algebraic proof of the complete integrability of the hierarchy, which we achieve by means of a factorization result for infinite matrices, that extends a result of M. Adler and P. Van Moerbeke [Commun. Math. Phys. 203 (1999) 185; 207 (1999) 589] for the case of (semi-infinite) moment matrices, and that we call a Borel decomposition.