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Spherical Monogenics: An Algebraic Approach

Authors:	P Van Lancker

Institution:	(1) Faculty of Applied Engineering Sciences, University College Ghent, Member of Ghent University Association, Schoonmeersstraat 52, 9000 Gent, Belgium

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 ${\mathcal{M}}_k$ . Received: October, 2007. Accepted: February, 2008.

Keywords:	" target="_blank"> Clifford analysis Dirac operators Representations Spin groups
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