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.
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Bougourzi, A.H., Vinet, L. On a bosonic-parafermionic realization of\(U_q (\widehat{sl(2)})\) . Lett Math Phys 36, 101–108 (1996). https://doi.org/10.1007/BF00714373
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DOI: https://doi.org/10.1007/BF00714373