On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model --- The Classical and Quantum Cases

Details On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model --- The Classical and Quantum Cases On the KP Hierarchy, $\hat{W}_{\infty}$ Algebra, and Conformal SL(2,R)/U(1) Model --- The Classical and Quantum Cases

1992-10-30

arxiv.org/abs/hep-th/9210162v1

Physics

High Energy Physics

High Energy Physics - Theory

(Invited talk given the second at the XXI International Conference on Differential Geometric Methods in Theoretical Physics, N

Scientific paper

We give a unified description of our recent results on the the inter-relationship between the integrable infinite KP hierarchy, nonlinear $\hat{W}_{\infty}$ current algebra and conformal noncompact $SL(2,R)/U(1)$ coset model both at the classical and quantum levels. In particular, we present the construction of a quantum version of the KP hierarchy by deforming the second KP Hamiltonian structure through quantizing the $SL(2,R)_k/U(1)$ model and constructing an infinite set of commuting quantum $\hat{W}_{\infty}$ charges (at least at $k$=1).

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