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\(R\)-matrix for cyclic representations of \(U_ q(\widehat{{\mathfrak sl}}(3,{\mathbb{C}}))\) at \(q^ 3=1\). (English) Zbl 0749.17013

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.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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