A new “dual” symmetry structure of the KP hierarchy

Abstract A new infinite set of commuting additional (“ghost”) symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding “ghost” and original KP-type Lax hierarchies connected to each other via a “duality” mapping exchanging the isospectral and “ghost” “times”. A new representation of the 2D Toda lattice hierarchy as a special Darboux-Backlund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eigenfunctions of the original KP subsystem.