## Abstract

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 e(6) and e(7) families of Lie algebras, and thus explain Westbury's [J. Phys. A 36, 2857 (2003)] observations about their uniform spectral decompositions. In doing so, we explore the extensions of the Brauer and symmetric group algebras to the centralizer algebras of e(7) and e(6) on their lowest-dimensional representations and (up to threefold) tensor products thereof, giving bases for them and a range of identities satisfied by the algebras' defining invariant tensors. (C) 2007 American Institute of Physics.

Original language | English |
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Article number | 103507 |

Pages (from-to) | Art. No. 103507 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2007 |

## Keywords

- FACTORIZED S-MATRICES
- 2 DIMENSIONS
- MODELS
- REPRESENTATIONS
- DIAGRAMS