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… 
View PDF on arXiv
7 Citations
Background Citations
1

7 Citations

REFERENCES ON SERIES OF LIE GROUPS

This is a list of published papers on series of Lie groups. It is intended to be complete but no doubt there are omissions. There are unpublished omissions. The principal ones are the papers by…

Diagrammatics for $F_4$

. We define a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type F…

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

Diagrammatics for F4$F_4$

Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters

We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in defining (minimal fundamental) and adjoint representations. By means of these…

Group theory

Group Theory: Birdtracks, Lie's, and Exceptional Groups

References

SHOWING 1-10 OF 41 REFERENCES

Fundamental representations of Yangians and singularities of R-matrices.

The construction of Ä-matrices is closely related to the representation theory of quantum groups. In particular, there is an important class of quantum groups, called Yangians, such that to every…

On tensor categories of Lie Type EN,N≠9☆

DEVELOPMENT OF A UNIFIED TENSOR CALCULUS FOR THE EXCEPTIONAL LIE ALGEBRAS

The uniformity of the decomposition law, for a family ℱ of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad⊗n of their adjoint representations ad is now well known.…

Spiders for rank 2 Lie algebras

A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidal…

Magic squares and matrix models of Lie algebras

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

Characterization of a Class of Cubic Forms

INVARIANT TENSORS AND DIAGRAMS

In this paper we first give three known examples of strict pivotal categories defined by a finite presentation. Then in the final section we give some of the relations for a conjectural strict…

Some indications that the exceptional groups form a series

for an appropriate value of as well as other uniform behavior of the exceptional Lie algebras with regard to the parameter Inspired by this P Deligne conjec tured that there might be a tensor…

Yang-Baxter equation and representation theory: I

The problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered. In caseN=2 all the solutions for arbitrarily finite-dimensional irreducible…