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

8 pages, Amslatex. The case for $U_q(\widehat{\mathfrak{s}l}(n))$ is added

Cited by in corpus (6)

• Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$
• Factorization of the Universal R-matrix for $U_q({\widehat{sl}}_2)$
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$
• Quantum current operators (III): Commutative quantum current operators, semi-infinite construction and functional models
• Generalized Drinfeld realization of quantum superalgebras and $U_q(\widehat{\mathfrak{o}sp}(1,2))$
• On the FRTS approach to quantized current algebras