@inbook{10.2307/j.ctt7rnjq.21,
ISBN = {9780691118369},
URL = {http://www.jstor.org/stable/j.ctt7rnjq.21},
abstract = {In this chapter, we determine all invariance groups whose primitive invariant tensors are$\delta _b^a $and fully symmetricdabc,dabc. The reduction of$V \otimes V$space yields a rule for evaluation of the loop contraction of fourd-invariants (18.9). The reduction of$V \otimes \bar V$yields the first Diophantine condition (18.13) on the allowed dimensions of the defining rep. The reduction ofV⊗V⊗Vtensors is straightforward, but the reduction ofA⊗Vspace yields the second Diophantine condition (d₄ in table 18.4) and limits the defining rep dimension ton≤ 27. The solutions of the two Diophantine conditions form},
bookauthor = {Predrag Cvitanović},
booktitle = {Group Theory: Birdtracks, Lie's, and Exceptional Groups},
pages = {190--209},
publisher = {Princeton University Press},
title = {E₆ family of invariance groups},
year = {2008}
}