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Recently, it has been established that the discrete star Laplace and thediscrete Dirac operator, i.e. the discrete versions of their continuouscounterparts when working on the standard grid, are rotation-invariant. Thiswas done starting from the Lie algebra so(m, C) corresponding to the specialorthogonal Lie group SO(m), considering its representation in the discreteClifford algebra setting and proving that these operators are symmetries of theDirac and Laplace operators. This set-up showed in an abstract way thatrepresentation-theoretically the discrete setting mirrors the EuclideanClifford analysis setting. However from a practical point of view, thegroup-action remains indispensable for actual calculations. In this paper, wedefine the discrete Spingroup, which is a double cover of SO(m), and considerits actions on discrete functions. We show that this group-action makes thespaces Hk and Mk into Spin(m)-representations. We will often consider thecompliance of our results to the results under the so(m, C)- action.

The Spingroup and its actions in discrete Clifford analysis