Nonlinear Ŵ∞ current algebra in the SL(2,R)/U(1) coset model

We show that in the world-sheet SL(2,R)/U(l) coset model there exists a hidden nonlinear W∞ current algebra, which incorporates all higher-spin (s≥ 2) currents including the energy-momentum tensor. Our proof is based on a free-field realization of Woo in terms of two scalars, as well as an elegant generating function for the W∞ currents in the classical model. After quantization, the deformed W∞ current algebra still results in an infinite set of commuting charges, which might be related to a space-time W∞symmetry for the 2D black hole arising in the corresponding string theory.