Let \(G\) be a totally minimal group, i.e., there does not exist a strictly coarser Hausdorff group topology on \(G\). The author associates to any representation on \(G\) an enveloping semigroup that is weakly almost periodic; hence semigroup theory may be used. If \(G\) is also connected, any unitary representation on \(G\) decomposes into finite-dimensional ones determined by the kernels of the corresponding subrepresentations, with all index coefficients vanishing at infinity. As an application the Fourier-Stieltjes algebra of a totally minimal group is shown to be uniformly dense in the \(C^*\)-algebra formed by all weakly almost periodic functions on the group.