  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 D, involving both forward and backward
differences, which factorizes the (discrete) Star-Laplacian (Delta = D^2). We
show how the space M_k of discrete homogeneous spherical monogenics of degree
k, is decomposable into 2^{2m-n} isomorphic irreducible representations with
highest weight (k + 1/2, 1/2,...,1/2) in the odd-dimensional case and two times
2^{2m-n} isomorphic irreducible representations with highest weight (k)'_+ = (k
+ 1/2, 1/2,...,1/2,1/2) resp. (k)'_- = (k + 1/2, 1/2,...,1/2,-1/2) in the even
dimensional case.
