GEOMETRIC REALIZATIONS OF REPRESENTATIONS OF FINITE-LENGTH

Let G = H x R-n be a semidirect product Lie group. We reduce the probl em of deciding which indecomposable representations of G may be realiz ed in subquotients of spaces of sections of vector bundles over infini tesimal neighborhoods of orbits of H in the dual of R-n to a problem i nvolving only representations of the H-stabilizers of the orbits.