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Cyclicity and R-matrices


Let \(S_1, \ldots , S_N\) simple finite-dimensional modules of a quantum affine algebra. We prove that if \(S_i\otimes S_j\) is cyclic for any \(i < j\) (i.e. generated by the tensor product of the highest weight vectors), then \(S_1\otimes \cdots \otimes S_N\) is cyclic. The proof is based on the study of R-matrices.

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The author would like to thank B. Leclerc and A. Moura for interesting comments and discussions. The author is supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement Number 647353 Qaffine.

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Hernandez, D. Cyclicity and R-matrices. Sel. Math. New Ser. 25, 19 (2019).

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  • Quantum affine algebras
  • Cyclic modules
  • Tensor product factorization

Mathematics Subject Classification

  • 17B37 (17B10, 81R50)