Abstract
Let g be a complex semisimple Lie algebra with Borel subalgebra b and corresponding nilradical n . We show that singular Whittaker modules M are simple if and only if the space Wh M of Whittaker vectors is 1-dimensional. For arbitrary locally n -finite g -modules V, an immediate corollary is that the dimension of Wh V is bounded by the composition length of V.
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