Spinor Spaces in Discrete Clifford Analysis

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 Z m , of the discrete Dirac operator ∂ , involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian. We show how the space M k of discrete spherical monogenics homogeneous of degree k , is decomposable into irreducible so ( m ) -representations.