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Cyclicity and R-matrices

Selecta Mathematica volume 25, Article number: 19 (2019) Cite this article

Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Sorbonne Paris Cité, Univ Paris Diderot, CNRS Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586, Batiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    David Hernandez

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Correspondence to David Hernandez.

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Hernandez, D. Cyclicity and R-matrices. Sel. Math. New Ser. 25, 19 (2019). https://doi.org/10.1007/s00029-019-0465-z

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  • DOI: https://doi.org/10.1007/s00029-019-0465-z

Keywords

  • Quantum affine algebras
  • Cyclic modules
  • Tensor product factorization

Mathematics Subject Classification

  • 17B37 (17B10, 81R50)