We dene an abelian group from the Dynkin diagram of a split real linear Lie group with abelian Cartan subgroups, G, and show that the R;0- groups dened by Knapp and Stein are subgroups of it. The proof relies on Vogan's approach to the R-groups. The R-group of a Dynkin diagram is easily computed just by looking at the diagram, and so it gives, for instance, quick proofs of the fact that the principal series with zero innitesimal character of the split groups E6, E8, G2 or F4 are irreducible. The Dynkin diagram subgroup also implicitly describes a small Levi subgroup, which we hope might play a role in computing regular functions on principal nilpotent orbits. We present in the end a conjecture and some evidence in this direction. The reducibility of principal series representations of real reductive Lie groups has been studied extensively. In the approach of Knapp and Stein (1), understanding the reducibility boils down to computing certain small abelian subgroups of the Weyl group, called R-groups. In the case when the group is linear and split, these R-groups can be described quite concretely. We will concentrate on a particular class of principal series for these split groups, those with innitesimal character equal to zero. They are obtained by parabolic induction as IndGMAN 0, for all representations ofM , which is a nite abelian group for all the cases which we will consider. There is an action of the Weyl group on the representations of M ,a nd representations in the same Weyl group conjugacy class yield isomorphic principal series. We show that we can reduce the understanding of the decomposition into irreducible components for all principal series with innitesimal character zero at once, to the same problem for a small Levi subgroup, which at the Lie algebra level consists of several copies of sl(2;R). The idea of reducing the understanding of the R-groups to SL(2;R )f or each was used by Knapp and Zuckermann (2) in their approach to the R-groups. We add to that approach the fact that, with a proper choice of a representative in each Weyl group conjugacy class, which we call acceptable, this reduction can be done simultaneously for all principal series with innitesimal character zero. As a by-product of this approach, we describe a nite group which we can con- struct combinatorially by looking at the Dynkin diagram of a simple split group, and show that each R;0 group has to be a subgroup of it (Theorem 1). As noted in the abstract, we believe that these results might also be useful in computing regular functions on principal nilpotent orbits. Such computations would be then