On the Kadomtsev-Petviashvili hierarchy, Ŵ∞ algebra, and conformal SL(2,R)/U(1) model. II. 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, algebra. This is achieved bx quantizing the conformal noncompact SL(2,R) k/ U(1) coset model, in which W, appears as a hidden current algebra. For the quantum W, 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∞, currents has played a crucial role in this exploration.