**Factorizations and Representations in a Finite Space** - Ady Mann

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers (the kq representation and related representations termed $q_{1}q_{2}$ representations (together with their conjugates)) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M.