Communications in Mathematical Physics

, Volume 178, Issue 1, pp 237–264 | Cite as

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

  • Edward Frenkel
  • Nikolai Reshetikhin


Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which areq-deformations of the classicalW. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Integrable Model 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Edward Frenkel
    • 1
  • Nikolai Reshetikhin
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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