Hou, Boyu; Shi, Kangjie; Yang, Zhongxia; Yue, Ruihong Integrable quantum chain and the representation of the quantum group SU\(_ q\)(2). (English) Zbl 0745.17021 J. Phys. A, Math. Gen. 24, No. 16, 3825-3836 (1991). Summary: We discuss the \(XXZ\) spin chain with certain boundary terms and the representation of the quantum group \(SU_ q(2)\). It is shown that Bethe ansatz states are highest-weight states of \(SU_ q(2)\). With a generic \(q\) we construct the irreducible representations of the quantum group. For \(q\) being a root of unity, we show that there are new Bethe ansatz states, which coincide with null states of \(SU_ q(2)\). By taking certain limits we can derive the state \(\mid b\rangle\), which is necessary for constructing the indecomposable but reducible representations of \(SU_ q(2)\) and for the completeness of the state space. In this case the Hamiltonian may not be completely diagonalized. Cited in 3 Documents MSC: 17B81 Applications of Lie (super)algebras to physics, etc. 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 82B23 Exactly solvable models; Bethe ansatz 17B37 Quantum groups (quantized enveloping algebras) and related deformations Keywords:Bethe ansatz states; irreducible representations; quantum group; spin chain models PDFBibTeX XMLCite \textit{B. Hou} et al., J. Phys. A, Math. Gen. 24, No. 16, 3825--3836 (1991; Zbl 0745.17021) Full Text: DOI