Spherical Monogenics: An Algebraic Approach

Abstract.

The space of spherical monogenics ${\mathcal{M}}_k$ in ${\mathbb{R}}^m$ can be regarded as a model for the irreducible representation of Spin(m) with weight $(k + \frac{1}{2}, \frac{1}{2}, \cdots , \frac{1}{2})$. In this paper we construct an orthonormal basis for ${\mathcal{M}}_k$. To describe the symmetry behind this procedure, we define certain Spin(m − 2)-invariant representations of the Lie algebra $\mathfrak{sl}$(2) on ${\mathcal{M}}_k$.