2010/12/22 by Richard Delanghe, Delanghe, Richard, Roman Lavicka +3
Mathematics · #30G35 #58A10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30G35 #msc:58A10
paper · pdf · doi:10.48550/arxiv.1012.4994
submitted
arxiv created 2010/12/22 · arxiv updated 2010/12/23
The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space Rm. 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.