Invariant Differential Operators and FCR factors of Enveloping algebras

Ian M. Musson, Jeb F. Willenbring

Published 2004-09-28, updated 2007-03-16Version 3

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.