A U(1) KAC-MOODY MODEL COUPLED TO 2D-GRAVITY

We consider a simple model of a scalar field with U(1) Kac-Moody local symmetry coupled to 2D-gravity in order to clarify the origin of Stuc kelberg symmetry in the w(infinity)-gravity theory. An analogous symme try takes place in our model too. The possible central extension of th e complete symmetry algebra and the corresponding critical dimension h ave been found. The analysis of the Hamiltonian and the constraints sh ows that the generators of the Kac-Moody, the reparametrization and th e Stuckelberg symmetries are not independent. The connection of the mo del with w1+infinity- and W1+infinity-gravity is discussed.