Journal of Statistical Physics

, Volume 102, Issue 3–4, pp 883–921 | Cite as

Free Field Construction for the ABF Models in Regime II

  • Michio Jimbo
  • Hitoshi Konno
  • Satoru Odake
  • Yaroslav Pugai
  • Jun'ichi Shiraishi


The Wakimoto construction for the quantum affine algebra U\(_q\)(\((\widehat{\mathfrak{s}\mathfrak{l}_2 })\)) admits a reduction to the q-deformed parafermion algebras. We interpret the latter theory as a free field realization of the Andrews–Baxter–Forrester models in regime II. We give multi-particle form factors of some local operators on the lattice and compute their scaling limit, where the models are described by a massive field theory with \(\mathbb{Z}\)\(_k\) symmetric minimal scattering matrices.

integrable lattice model ABF model in regime II free field construction vertex operator approach q-deformed parafermion form factor \(\mathbb{Z}\)\(_k\) symmetric scattering deformed W algebra 


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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Michio Jimbo
    • 1
  • Hitoshi Konno
    • 2
  • Satoru Odake
    • 3
  • Yaroslav Pugai
    • 4
  • Jun'ichi Shiraishi
    • 5
  1. 1.Division of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  2. 2.Department of Mathematics, Faculty of Integrated Arts and SciencesHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Department of Physics, Faculty of ScienceShinshu UniversityMatsumotoJapan
  4. 4.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  5. 5.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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