The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
arXiv:1012.4994
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.
arXiv commentsubmitted
References in corpus (6)
- Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3
- On Appell Sets and the Fueter-Sce Mapping
- The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
- The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces
- On polynomial solutions of generalized Moisil-Theodoresco systems and Hodge-de Rham systems
- Fischer decomposition by inframonogenic functions