G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of
a polarized algebraic variety to the existence of a Kahler metric of constant
scalar curvature. In [Don02] Donaldson partially confirmed it in the case of
projective toric varieties. In this paper we extend Donaldson's results and
computations to a new case, that of reductive varieties.
The changes in the second version are cosmetic
