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 \({\mathcal{M}}_k\).
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This paper is dedicated to the memory of our friend and colleague Jarolim Bureš
Received: October, 2007. Accepted: February, 2008.
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Van Lancker, P. Spherical Monogenics: An Algebraic Approach. AACA 19, 467–496 (2009). https://doi.org/10.1007/s00006-009-0168-1
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DOI: https://doi.org/10.1007/s00006-009-0168-1