Abstract
In this paper we work in the `split' discrete Cli fford analysis setting, i.e. the m-dimensional function theory concerning null-functions of the discrete Dirac operator d, defi ned on the grid Zm, involving both forward and backward di fferences. This Dirac operator factorizes the (discrete) Star-Laplacian (Delta*= d2). We show how the space Hk of discrete k-homogeneous spherical harmonics, which is a reducible so(m;C)-representation, may explicitly be decomposed into 2^2m isomorphic copies of irreducible so(m;C)-representations with highest weight (k, 0, ..., 0). The key element is the introduction of 2^2m idempotents, dividing the discrete Cli fford algebra in 2^2m subalgebras of dimension (k+m-1,k) - (k+m-3, k).
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