Symmetric Presentations of Coxeter Groups more

The remarkable techniques of symmetric generation have furnished several almost effortless constructions of many exceptional objects by exhibiting highly symmetric generating sets for groups. In particular, these generating sets often provide symmetric presentations for these groups. In this short talk, we will show how the familiar Coxeter-Moser presentations for the Coxeter groups of types A_n, D_n, and even the exceptional cases E_6, E_7, and E_8, may be naturally derived as symmetric presentations in an almost uniform manner. In doing so, we will construct representations of these groups with some striking properties.