There is a natural connection between particle physics and representation theory. In particular, we often embed the Standard Model in a larger gauge group (such as in Grand Unified Theories) and spontaneously break the symmetry back down to the Standard Model at low energies. Particles naturally live in representations of this larger gauge group, and the branching rules of these representations tell us how GUT representations break into Standard Model representations. Hence, the computation of these branching rules tells us much about the physics of these theories.

In this talk, I will first give an introduction to the necessary details about Lie algebras, discuss their internal structure and representations, and explain what precisely we mean by "branching rules" and how one would compute these rules. The second part of the talk will focus on my previous work at Vanderbilt on the LieART (Lie Algebras and Representation Theory) Mathematica program, extending it to compute almost all branching rules.