Rational R-matrices, centralizer algebras and tensor identities for e_6 and e_7 exceptional families of Lie algebras

N. J. MacKay; A. Taylor

doi:10.1063/1.2779960

paper

Rational R-matrices, centralizer algebras and tensor identities for e_6 and e_7 exceptional families of Lie algebras

arXiv:math/0608248 · doi:10.1063/1.2779960

Abstract

We use Cvitanovic's diagrammatic techniques to construct the rational solutions of the Yang-Baxter equation associated with the $e_{6}$ and $e_{7}$ families of Lie algebras, and thus explain Westbury's 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 three-fold) tensor products thereof, giving bases for them and a number of identities satisfied by the algebras' defining invariant tensors.

24 pages. More minor corrections

References in corpus (1)

Representation theory for dilute lattice models