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Spinor-valued and Clifford algebra-valued harmonic polynomials. (English) Zbl 0972.43005

In the paper under review the author gives some decompositions of the spinor-valued and Clifford algebra-valued harmonic polynomials on \( \mathbb{R} ^n \) and proves that each component of the decompositions is an irreducible representation space with respect to the Lie group \( \text{Spin} (n) \).

MSC:

43A85 Harmonic analysis on homogeneous spaces
43A90 Harmonic analysis and spherical functions
58J05 Elliptic equations on manifolds, general theory
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