Abstract: In semisimple Lie group theory, the most accessible unitary representations are the principal series representations. These are the representations unitarily induced from representations of minimal parabolic subgroups. Now let G be an infinite dimensional simple direct limit Lie group, for example SL(∞,R), Sp(17,∞) or SO(∞,∞), say G = lim G_n. If a minimal parabolic subgroup P in G is the limit of minimal parabolics P_n in the G_n, and if one is careful, then some principal series representations of G can be constructed as direct limits of principal series representations of the G_n. This sidesteps the problems caused by lack of Haar measure on G. But most (in some sense almost all) parabolics in G are more complicated, and one needs a substitute for Haar measure. I'll describe the structure of minimal parabolics in general and the use of amenability to carry out the induction step for construction of principal series representations.