Higgs potentials as a consequence of extra space-time dimensions (Q1092438)

We study the dimensional reduction of multidimensional ``free'' gauge theories with an additional space-time symmetry. Within the framework of this approach a general method for finding explicitly the scalar fields in a reduced theory is developed. The fields are described by an intertwining operator the construction of which can be carried out by a root lattice technique which is elaborated for complex classical Lie algebras and generalizes the technique of Dynkin diagrams.