charge space symmetries. On the other side, string theory starts from the quantum fields and implements the generalization from point particles to extended particles, like a one dimensional string or the higher dimensional branes. This also leads to discrete spectra, and a more complete description of unification physics. But this unification picture is more complicated because the strings are defined over a spacetime manifold, which leads to fundamental problems and the search for a more fundamental $(M-)$theory, where one hopes to understand the existence of a spacetime manifold itself as the emergent property of a specific vacuum rather than an identifiable feature of the underlying theory [@Schwarz]. A partner approach of string theory, but less ambitious, is the Lie algebraic unification program, as in $E_8$ unification [@LisiLieE8; @E8CarlosonTony]. This makes use of the generalization of the simplest non-abelian gauge symmetry, $SU(2)$, to higher-dimensional ones, ending with a complete unification of the charge Lie group symmetries of the standard model in the largest exceptional Lie algebra $E_8$, making heavy use of the representation theory of these algebras. Our aim is to use this unification aspect of the representation theory of Lie algebras to improve the spin foam approach of LQG. We 