ALGEBRA OF PSEUDODIFFERENTIAL-OPERATORS AND SYMMETRIES OF EQUATIONS IN THE KADOMTSEV-PETVIASHVILI HIERARCHY

Point symmetries are obtained for all equations in the KP hierarchy. T he Lie algebra far each equation is infinite dimensional and involves several arbitrary functions of the corresponding time t(N). The symmet ry algebra is a semidirect sum of a Virasoro algebra and a Kac-Moody o ne. The ''positive'' part of this algebra is embedded into the known W -infinity algebra of KP symmetries and into the free fermion algebra < (g)over cap l>(infinity). The corresponding action on the tau-function is presented. The negative part of the point symmetries does not fit into the free fermion algebra, but is embedded into a P-infinity algeb ra, based on the algebra of pseudodifferential operators. (C) 1997 Ame rican Institute of Physics.