  For the diagonalization of the Hamilton matrix in the Heisenberg model
relevant dimensions are determined depending on the applicable symmetries.
Results are presented, both, by general formulae in closed form and by the
respective numbers for a variety of special systems. In the case of cyclic
symmetry, diagonalizations for Heisenberg spin rings are performed with the use
of so-called magnon states. Analytically solvable cases of small spin rings are
singled out and evaluated.
