@inbook{10.2307/j.ctt7rnjq.22,
ISBN = {9780691118369},
URL = {http://www.jstor.org/stable/j.ctt7rnjq.22},
abstract = {In this chapter we classify and construct all invariance groups whose primitive invariant tensors are a symmetric bilineardab, and a symmetric trilineardabc, satisfying the relation (19.16).Take as primitives a symmetric quadratic invariantdaband a symmetric cubic invariantdabc. As explained in chapter 12, we can usedabto lower all indices. In the birdtrack notation, we drop the open circles denoting symmetric 2-index invariant tensordab, and we drop arrows on all lines:The definingn-dimensional rep is by assumption irreducible, soWere (19.3) nonvanishing, we could use to project out a 1-dimensional subspace, violating the},
bookauthor = {Predrag Cvitanović},
booktitle = {Group Theory: Birdtracks, Lie's, and Exceptional Groups},
pages = {210--217},
publisher = {Princeton University Press},
title = {F₄ family of invariance groups},
year = {2008}
}