On the annihilator ideal of a highest weight vector

Details On the annihilator ideal of a highest weight vector On the annihilator ideal of a highest weight vector

2010-03-18

arxiv.org/abs/1003.3522v4

Mathematics

Representation Theory

Scientific paper

In this paper the annihilator ideal ann(v) of a highest weight vector v in an arbitrary finite dimensional irreducible SL(E)-module V is studied. We compute the complement W in U(sl(E)) of the l'th piece of the canonical filtration of ann(v) and express the complement W as the universal enveloping algebra of a Lie algebra n defined in terms of a flag F in E. We use this calculation to study the l'th piece of the canonical filtration U(sl(E))v in V determined by the highest weight vector v.

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