Bijection between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins   $\sigma=\frac{p-1}{2}$
  We propose a general method by which a spin-$S$ is decomposed into spins less than $S$. We have obtain the exact mapping between spin $S=\frac{p^{M}-1}{2}$ and a cluster of $M$ spins $\sigma=\frac{p-1}{2}$. We have discuss the possible applications of such transformations. In particular we have show how a general $d+1$ dimensional spin-$\frac{p-1}{2}$ model with general interactions can be reduced to $d$-dimensional spin-$S$ model with $S=\frac{p^{M}-1}{2}$. 
N. Sh. Izmailian, Onofre Rojas and S. M. de Souza
math-ph cond-mat.stat-mech math.MP