Rational R-matrices, centralizer algebras and tensor identities for e6 and e7 exceptional families of Lie algebras

@article{Mackay2006RationalRC,
  title={Rational R-matrices, centralizer algebras and tensor identities for e6 and e7 exceptional families of Lie algebras},
  author={Niall J. Mackay and Arthur Taylor},
  journal={Journal of Mathematical Physics},
  year={2006},
  volume={48},
  pages={103507-103507}
}
We use Cvitanovic’s [Group Theory (Princeton University Press, Princeton, NJ, in press) (http://www.nbi.dk/GroupTheory/); Phys. Rev. D 14, 1536 (1976)] diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation [Yang-Baxter Equation in Integrable Systems, edited by M. Jimbo, Advanced Series in Mathematical Physics Vol. 10 (World scientific, Singapore, 1990)] associated with the e6 and e7 families of Lie algebras, and thus explain Westbury’s [J. Phys. A 36, 2857… 

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