Date, E.; Jimbo, M.; Miki, K.; Miwa, T. \(R\)-matrix for cyclic representations of \(U_ q(\widehat{{\mathfrak sl}}(3,{\mathbb{C}}))\) at \(q^ 3=1\). (English) Zbl 0749.17013 Phys. Lett., A 148, No. 1-2, 45-49 (1990). Summary: For \(q\) an \(N\)-th root of unity we give an \(N^{n-1}\)-dimensional representation of \(U_ q(\widehat{sl}(n,\mathbb{C}))\). Restricting to the case \(n=3\), \(N=3\) we then construct a trigonometric \(R\) matrix which intertwines tensor products of two such representations. Cited in 13 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory Keywords:quantum group; trigonometric \(R\) matrix PDFBibTeX XMLCite \textit{E. Date} et al., Phys. Lett., A 148, No. 1--2, 45--49 (1990; Zbl 0749.17013) Full Text: DOI References: [1] Drinfeld, V. G., (Proc. ICM Berkeley (1987)), 798 [2] Jimbo, M., Lett. Math. Phys., 10, 63 (1985) [3] Bazhanov, V. V.; Stroganov, Yu. G., J. Stat. Phys., 51, 799 (1990) [4] Fateev, V. A.; Zamolodchikov, A. B., Phys. Lett. A, 92, 492 (1982) [5] Babelon, O., Nucl. Phys. B, 230, 241 (1984) [6] Bazhanov, V. V.; Kashaev, R. M., Cyclic \(L\) operators related with 3-state \(R\)-matrix (1990), preprint · Zbl 0747.17015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.