Abstract

Let G = H ×_sRⁿ be a semidirect product Lie group, let Ø be a locally closed orbit of H in the dual of Rⁿ, and let S be the subgroup of H stabilizing some point of Ø. Suppose that U is a  of length n + 1 of G, such that every irreducible representation in the composition series of U is associated to the orbit Ø and a finite dimensional  of S by the Mackey machine. We prove that if H is a real linear algebraic group, S is an algebraic subgroup of H, and all finite dimensional s of S are rational, then U may be realized as a subquotient of the canonical  of G in the space of functions on the n^th-order infinitesimal neighborhood of Ø in its ambient vector space, taking values in some finite dimensional  of H.

Authors