Quantum current operators (III): Commutative quantum current operators, semi-infinite construction and functional models

摘要

We construct a commutative current operator $\bar x^+(z)$ inside$U_q(\hat{\frak sl}(2))$. With this operator and the condition of quantumintegrability on the quantum current of $U_q(\hat{\frak sl}(2))$, we derive thequantization of the semi-infinite construction of integrable modules of$\hat{\frak sl}(2)$ with the current operator $e(z)$ of $\hat{\frak sl}(2)$.The quantization of the functional models for $\hat{\frak sl}(2)$ are alsogiven.