In this thesis a charged scalar field coupled to a Landau-gauge Yang-Mills theory hasbeen investigated. Among others, the confinement problem serves as a motivation. Thestrong interaction force can be described by an attractive potential. This potential de-pends on the gauge group as well as on the representation chosen for the scalar. In thiscase, the adjoint and the fundamental representation are considered. The aim of this thesiswas to examine whether these differences can be seen on the level of correlation functions.To this end, the Dyson-Schwinger equations for both systems were derived first. Asexpected, they turn out to be topologically equivalent and no difference can be seen.Next, an infrared powercounting analysis was performed on the adjoint and the fun-damental case. The leading diagrams of each DSE were identified and their infraredexponents were evaluated. In addition, the possible phases of the system were discussed,along with the mathematically possible solutions. However, the IREs of both systems areidentical and lead to the same solutions in both cases.To gain further insight, the colour structure of the diagrams appearing in the DSEswas analysed. A one-loop truncation was applied.The colour structures of the remaining diagrams were calculated in terms of groupinvariants and later the values for the groups SU(2), SU(3) and G(2) were inserted.In the following, the results for the leading and quenched diagrams are presented.At the end, the differences occuring in non-leading contributions are discussed.By identifying the contributions that are sensitive to different gauge groups one pro-vides the basis to identify the mechanism by more sophisticated treatments, in particularself-consistent extensions. In particular, this gives reason to believe that the qualitativelydifferent behaviour of the string tension could be embodied in (low-n) correlation functions.