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