VIRASORO SYMMETRY OF CONSTRAINED KP HIERARCHIES

The conventional formulation of additional nonisospectral symmetries f or the full Kadomtsev-Petviashvili (KP) integrable hierarchy is not co mpatible with the reduction to the important class of constrained KP ( cKP) integrable models. This paper solves explicitly the problem of co mpatibility of the Virasoro part of additional symmetries with the und erlying constraints of cKP hierarchies. Our construction involves an a ppropriate modification of the standard additional-symmetry Rows by ad ding a set of ''ghost symmetry'' Rows. We also discuss the special cas e of cKP - truncated KP hierarchies, obtained as Darboux-Backlund orbi ts of initial purely differential Lax operators. Our construction esta blishes the condition for commutativity of the additional-symmetry flo ws with the discrete Darboux-Backlund transformations of cKP hierarchi es leading to a new derivation of the string-equation constraint in ma trix models. (C) 1997 Published by Elsevier Science B.V.