Quantum Current Operators-I Zeros and Poles of Quantum Current Operators and the Condition of Quantum Integrability

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 study the zeros and poles of the quantum current operators and present a condition of integrability on the quantum current operators of $U_q(\widehat{\mathfrak{sl}}(2))$, which is a deformation of the corresponding condition for $\widehat{\mathfrak{sl}}(2)$. We also present the results about the zeros and poles of the quantum current operators of $U_q(\widehat{\mathfrak{sl}}(n))$.