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

1995/05/22 by Edward Frenkel, Nicolai Reshetikhin, Nikolai Reshetikhin · 7 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math.QA #q-alg

paper · pdf · doi:10.1007/bf02104917

31 pages, AMSLATEX

arxiv created 1995/05/22 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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)^.

Citations

• Fock representations of the affine Lie algebraA 1 (1)

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