Counting one-codimensional subspaces generated by subsets of a root system (Q2901388)

Let \(\Phi\) be an irreducible reduced root system in a Euclidean space \(E\). The authors give a complete classification of one-codimensional subspaces of \(E\) generated by subsets of \(\Phi\). A basis for each such subspace is given explicitly for the classical types. For exceptional types (except \(G_2\)), the calculations are done using computer. The paper is concluded with an application to the classification theory of semisimple finite prehomogeneous vector spaces.