Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

  • Ben CoxEmail author
  • Vyacheslav Futorny
  • Renato Alessandro Martins
Part of the Developments in Mathematics book series (DEVM, volume 38)


We use the description of the universal central extension of the DJKM algebra \(\mathfrak{s}\mathfrak{l}(2,R)\) where \(R = \mathbb{C}[t,t^{-1},u\,\vert \,u^{2} = t^{4} - 2ct^{2} + 1]\) given in [CF11] to construct realizations of the DJKM algebra in terms of sums of partial differential operators.

Key words

Wakimoto modules DJKM algebras Affine Lie algebras Fock spaces 

Mathematics Subject Classification (2010):

17B65 17B69. 



The first author would like to thank the other two authors and the University of São Paulo for hosting him while he visited Brazil in June of 2013 where part of this work was completed. The second author was partially supported by Fapesp (2010/50347-9) and CNPq (301743/2007-0). The third author was supported by FAPESP (2012/02459-8).


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ben Cox
    • 1
    Email author
  • Vyacheslav Futorny
    • 2
  • Renato Alessandro Martins
    • 2
  1. 1.Department of MathematicsThe College of CharlestonCharlestonUSA
  2. 2.Departamento de MatemáticaInstituto de Matemática e EstatísticaSão PauloBrasil

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