Construction and Characterization of Representations of SU(7) for GUT Model Builders

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.