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

Abstract

We construct a commutative current operator ${\bar{x}}^{+}(z)$ inside $U_q(\widehat{\mathfrak{s}l}(2))$. With this operator and the condition of quantum integrability on the quantum current of $U_q(\widehat{\mathfrak{s}l}(2))$, we derive the quantization of the semi-infinite construction of integrable modules of $\widehat{\mathfrak{s}l}(2)$ with the current operator $e(z)$ of $\widehat{\mathfrak{s}l}(2)$. The quantization of the functional models for $\widehat{\mathfrak{s}l}(2)$ are also given.

12 pages Amslatex

References in corpus (1)

• Zeros and poles of quantum current operators and the condition of quantum integrability

Cited by in corpus (2)

• Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$