  We prove that special ample line bundles on toric varieties arising from root
systems are projectively normal. Here the maximal cones of the fans correspond
to the Weyl chambers, and special means that the bundle is torus-equivariant
such that the character of the line bundle that corresponds to a maximal Weyl
chamber is dominant with respect to that chamber. Moreover, we prove that the
associated semigroup rings are quadratic.
