Division Algebra Representations of SO(4,2)

Representations of $\text{SO}(4,2)$ are constructed using $4\times 4$ and $2\times 2$ matrices with elements in ${\mathbb{H}}^{\mathrm{\prime }}\otimes \mathbb{C}$, and the known isomorphism between the conformal group and $\text{SO}(4,2)$ is written explicitly in terms of the $4\times 4$ representation.