Difference equations of quantum current operators and quantum parafermion construction

Abstract

For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\widehat{\mathfrak{s}l}(2))$ of level $k+1$, $x^{\pm }(z)x^{\pm }(z{q}^{\pm 2})\cdot \cdot \cdot x^{\pm }(z{q}^{\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\widehat{\mathfrak{s}l}(2))$.

15 pages Amslatex

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