A New ``Dual'' Symmetry Structure of the KP Hierarchy

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 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.