ON THE KADOMTSEV-PETVIASHVILI HIERARCHY, (W)OVER-CAP INFINITY ALGEBRA, AND CONFORMAL SL(2,R)/U(1) MODEL .2. THE QUANTUM CASE

This article is devoted to constructing a quantum version of the famous Kadomtsev-Petviashvili (KP) hierarchy by deforming its second Hamiltonian structure, namely, the nonlinear W(infinity) algebra. This is achieved by quantizing the conformal noncompact SL (2,R) k/U ( 1) coset model, in which W(infinity) appears as a hidden current algebra. For the quantum W(infinity) algebra at level k = 1, an infinite set of commuting quantum charges in explicit and closed form was successfully constructed. Using them, a completely integrable quantum KP hierarchy is constructed in the Hamiltonian form. A two-boson realization of the quantum W(infinity) currents has played a crucial role in this exploration.