The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
Complex Variables
2010-12-23 v1
Abstract
The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space R^m. As is well-known, it can be understood as an irreducible decomposition with respect to the so-called L-action of the Pin group Pin(m). But, on Clifford algebra valued polynomials, we can consider also the H-action of Pin(m). In this paper, the corresponding Fischer decomposition for the H-action is obtained. It turns out that, in this case, basic building blocks are the spaces of homogeneous solutions to the Hodge-de Rham system. Moreover, it is shown that the Fischer decomposition for the H-action can be viewed even as a refinement of the classical one.
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Cite
@article{arxiv.1012.4994,
title = {The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces},
author = {Richard Delanghe and Roman Lavicka and Vladimir Soucek},
journal= {arXiv preprint arXiv:1012.4994},
year = {2010}
}
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