Quantum Current Operators-II 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 $U_q(\widehat{\mathfrak{sl}}(2))$ of level $k+1$, $x^{\pm }(z)x^{\pm }(z{q}^{\pm 2})\cdots x^{\pm }(z{q}^{\pm 2k})$ are vertex operators satisfying certain q-difference equations, and we derive the quantum parafermions of $U_q(\widehat{\mathfrak{sl}}(2))$.