Representations of Finite Length of Semidirect Product Lie Groups

We treat a part of the program of studying the correspondence between orbits and representations of finite length. In Section 1 we prove that it is possible to divide a regular distribution by a function so that the quotient is a regular distribution, under suitable conditions on the function. In Section 2 the results of Section 1 are used to prove that all representations of finite flag length of a vector group, realized in a vector bundle over a submanifold of the dual, act by endomorphisms of the bundle. In Section 3 the results of Section 2 are used to give an extension of the Mackey functor to representations of semidirect product Lie groups with a fixed composition series.