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Spherical monogenics: An algebraic approach. (English) Zbl 1172.30030

Summary: The space of spherical monogenics \({\mathcal{M}}_k\) in \({\mathbb{R}}^m\) can be regarded as a model for the irreducible representation of \(\text{Spin}(m)\) with weight \((k + \frac{1}{2}, \frac{1}{2}, \dots , \frac{1}{2})\). 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 \({\mathcal{M}}_k\).

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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