Loop Algebra Symmetries and Commuting Flows for the   Kadomtsev-Petviashvili Hierarchy
  The relation between the $\widehat\gl(\infty)$ symmetry of the Kadomtsev-Petviashvili hierarchy and the Kac-Moody-Virasoro Lie point symmetries of the individual equations is established. The Lie point symmetries are shown to be the only local ones. 
A. Yu. Orlov and P. Winternitz