Weight diagrams of $G_2$

This post contains pictures of weight diagrams of irreducible representations of the Lie algebra $G_2$.

The 7-dimensional representation of $G_2$

The exceptional Lie algebra $G_2$ has an irreducible representation of dimension 7. In this post I calculate the matrices of this irrep.

Commutation relations in $G_2$

In this post I calculate the structure constants of the exceptional Lie algebra $G_2$. I assume the reader is familiar with Lie algebras, for example at the level of chapter 9 in [1].