An affine variety with an action of a semisimple group G is called “small” if every nontrivial G-orbit in X is isomorphic to the orbit of a highest weight vector. Such a variety X carries a canonical action of the multiplicative group commuting with the G-action. We show that X is determined by the -variety of fixed points under a maximal unipotent subgroup . Moreover, if X is smooth, then X is a G-vector bundle over the algebraic quotient .

If G is of type (), , , , or , we show that all affine G-varieties up to a certain dimension are small. As a consequence, we have the following result. If , every smooth affine -variety of dimension is an -vector bundle over the smooth quotient , with fiber isomorphic to the natural representation or its dual.