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If is a semisimple Lie algebra, we describe the prime factors of () 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 ()-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.
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Musson et al. (2008) studied this question.
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