  If $\fg$ 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.
