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arXiv · 1010.1620

Orthogonal basis for spherical monogenics by step two branching

R. Lavicka·V. Soucek·P. Van Lancker
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Abstract

Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on R^m. Fix the direct sum R^m = R^p x R^q. In this paper we will study the decomposition of the space M_n(R^m;C_m) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result we obtain a Spin(p) x Spin(q)-invariant orthonormal basis for M_n(R^m;C_m). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M_n(R^m;C_m).

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R. Lavicka, V. Soucek, P. Van Lancker. 2010-10-08. Orthogonal basis for spherical monogenics by step two branching. https://arxiv.org/abs/1010.1620

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