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We generalize some results concerning affine algebras at the critical levelto the corresponding quantum algebras. In particular, we show that the Wakimotorealization provides a homomorphism of Poisson algebras from the center of aquantum affine algebra to a Heisenberg-Poisson algebra. This homomorphism is aq-deformation of the Miura transformation. It is given by the same formulas asthe spectra of transfer-matrices of the corresponding quantum integrablemodels. The image of the center in the Heisenberg-Poisson algebra is a Poissonsubalgebra of the latter, which is a q-deformation of the correspondingclassical W-algebra. The relations in this Poisson algebra are explicitlycomputed in the case of sl(n)^.Comment: 31 pages, AMSLATE

Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1