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arXiv · 1310.3346

Multiplicity-free primitive ideals associated with rigid nilpotent orbits

Alexander Premet
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Abstract

We prove that any finite W-algebra U(g,e) admits a one-dimensional representation fixed by the action of the component group of the centraliser of e. As a consequence, for any nilpotent orbit O in g there exists a multiplicity-free (and hence completely prime) primitive ideal of the universal enveloping algebra U(g) whose associated variety coincides with the Zariski closure of O.

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Alexander Premet. 2014-01-10. Multiplicity-free primitive ideals associated with rigid nilpotent orbits. https://arxiv.org/abs/1310.3346

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