Communications in Mathematical Physics

, Volume 349, Issue 1, pp 271–283 | Cite as

A New Braid-like Algebra for Baxterisation

  • N. CrampeEmail author
  • L. Frappat
  • E. Ragoucy
  • M. Vanicat


We introduce a new Baxterisation for R-matrices that depend separately on two spectral parameters. The Baxterisation is based on a new algebra, close to but different from the braid group. We study representations of this new algebra on the vector space \({(\mathbb{C}^m)^{\otimes n}}\), when the generators act locally. The ones for \({m=2}\) are completely classified. We also introduce some representations for generic m: they allow us to recover the R-matrix of the multi-species generalization of the totally asymmetric simple exclusion process with different hopping rates.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.L2C, UMR 5221 CNRS-Université de MontpellierMontpellierFrance
  2. 2.LAPTh, CNRS–Université de Savoie Mont BlancAnnecy-le-Vieux CedexFrance

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