Geodesic
A TWISTED APPROACH TO KOSTANT'S PROBLEM
Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 549-561

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DOI

We use Arkhipov's twisting functors to show that the universal enveloping algebra of a semi-simple complex finite-dimensional Lie algebra surjects onto the space of ad-finite endomorphisms of the simple highest weight module $L(\lambda)$, whose highest weight is associated (in the natural way) with a subset of simple roots and a simple root in this subset. This is a new step towards a complete answer to a classical question of Kostant. We also show how one can use the twisting functors to reprove the classical results related to this question.
DOI : 10.1017/S0017089505002776
Mots-clés : 17B10, 17B35, 17B20 
MAZORCHUK, VOLODYMYR. A TWISTED APPROACH TO KOSTANT'S PROBLEM. Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 549-561. doi: 10.1017/S0017089505002776
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