Fermions Acting on Quasi-local Operators in the XXZ Model

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)


This is a survey about the construction of fermions which act on the space of quasi-local operators in the XXZ model. We also include a proof of the anti-commutativity of fermionic creation operators.


Transfer Matrix Local Operator Primary Operator Vertex Model Infinite Lattice 
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Research of M.J. is supported by the Grant-in-Aid for Scientific Research B-23340039. Research of T.M. is supported by the Grant-in-Aid for Scientific Research B-22340031. Research of F.S. is supported by RFBR-CNRS grant 09-02-93106 and DIADEMS program (ANR) contract number BLAN012004. The authors would like to thank the organisers of the workshops “Infinite Analysis 11—Frontier of Integrability—” at Tokyo and “Symmetries, Integrable Systems and Representations” at Lyon, for invitation and kind hospitality. With sincere gratitude for what they got from him, T.M. and F.S. would like to express their heartiest congratulations to Professor Michio Jimbo on his 60th birthday.


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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of MathematicsRikkyo UniversityToshima-ku, TokyoJapan
  2. 2.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  3. 3.Laboratoire de Physique Théorique et Hautes EnergiesUniversité Pierre et Marie CurieParis Cedex 05France

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