Starting from the representation of the $(n-1)+n-$dimensional Lorentz pseudo-sphere on the projective space $\mathbb{ P}\mathbb{ R}^{ n,n}$, we propose a method to derive a class of solutions underlying to a Dirac-K\"ahler type equation on the lattice. We make use of the Cayley transform $\varphi({ \bf w})=\dfrac{ 1+{ \bf w}}{ 1-{ \bf w}}$ to show that the resulting group representation arise from the same mathematical framework as the conformal group representation in terms of the { \it general linear group} $GL\left(2,\Gamma(n-1,n-1)\cup\{ 0\}\right)$. That allows us to describe such class of solutions as a commutative $n-$ary product, involving the quasi-monomials $\varphi\left({ \bf z}_j\right)^{ -\frac{ x_j}{ h}}$ ($x_j \in h\mathbb{ Z}$) with membership in the paravector space $\mathbb{ R}\oplus \mathbb{ R}{ \bf e}_j{ \bf e}_{ n+j}$.
Categories: math-ph math.CV math.MP