Quantum Affine Algebras and Deformations of the Virasoro and W-algebras

Details Quantum Affine Algebras and Deformations of the Virasoro and W-algebras Quantum Affine Algebras and Deformations of the Virasoro and W-algebras

1995-05-22

arxiv.org/abs/q-alg/9505025v1

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, AMSLATEX

Scientific paper

10.1007/BF02104917

We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a homomorphism of Poisson algebras from the center of a quantum affine algebra to a Heisenberg-Poisson algebra. This homomorphism is a q-deformation of the Miura transformation. It is given by the same formulas as the spectra of transfer-matrices of the corresponding quantum integrable models. The image of the center in the Heisenberg-Poisson algebra is a Poisson subalgebra of the latter, which is a q-deformation of the corresponding classical W-algebra. The relations in this Poisson algebra are explicitly computed in the case of sl(n)^.

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