Spinor Spaces in Discrete Clifford Analysis

Abstract

In this paper we work in the ‘split’ discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid $${\mathbb {Z}}^m$$ , of the discrete Dirac operator $${\partial }$$ , involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian. We show how the space $${\mathcal {M}}_k$$ of discrete spherical monogenics homogeneous of degree k, is decomposable into irreducible $$\mathfrak {so}(m)$$ -representations.