  Let G be the (special) affine group, semidirect product of SL_n and C^n. In
this paper we study the representation theory of G and in particular the
question of rationality for V/G where V is a generically free G-representation.
We show that the answer to this question is positive if the dimension of V is
sufficiently large and V is indecomposable. We have a more precise theorem if V
is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.
