The Lie algebra ${\mathfrak{sl}}_4(\mathbb{C})$ and the hypercubes

William J. Martin, Paul Terwilliger

We describe a relationship between the Lie algebra ${\mathfrak{sl}}_4(\mathbb{C})$ and the hypercube graphs. Consider the $\mathbb{C}$-algebra $P$ of polynomials in four commuting vari…