A twisted approach to Kostant's problem

Details A twisted approach to Kostant's problem A twisted approach to Kostant's problem

2005-04-03

arxiv.org/abs/math/0504041v1

Glasg. Math. J. 47 (2005), no. 3, 549-561

Mathematics

Representation Theory

16 pages

Scientific paper

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.

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