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On the KP Hierarchy, Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case
This paper is devoted to constructing a quantum version of the famous KP
hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear
algebra. This is achieved by quantizing the conformal
noncompact coset model, in which appears
as a hidden current algebra. For the quantum algebra at
level , we have succeeded in constructing an infinite set of commuting
quantum charges in explicit and closed form. Using them a completely integrable
quantum KP hierarchy is constructed in the Hamiltonian form. A two boson
realization of the quantum currents has played a crucial
role in this exploration.Comment: 33
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