2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125738If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also determine, which finite dimensional $\mcU(\fg)$-modules are modules over a given prime factor. As an application we study finite dimensional modules over some rings of invariant differential operators arising from Howe duality.15 pages, updated versionRepresentation Theorytext