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Letters in Mathematical Physics

, Volume 36, Issue 2, pp 101–108 | Cite as

On a bosonic-parafermionic realization of\(U_q (\widehat{sl(2)})\)

  • A. Hamid Bougourzi
  • Luc Vinet
Article

Abstract

We realize the\(U_q (\widehat{sl(2)})\) current algebra at an arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limitq→1. Our realization coincides with those of Frenkel-Jing and Bernard when the levelk takes the values 1 and 2, respectively.

Mathematics Subject Classification (1991)

81R10 81T40 22E65 

Key words

bosonic fields parafermionic fields free-field realization quantum affine algebra 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • A. Hamid Bougourzi
    • 1
  • Luc Vinet
    • 1
  1. 1.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada

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