Multiplicity-free primitive ideals associated with rigid nilpotent orbits
Representation Theory
2014-01-13 v3 Rings and Algebras
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.
Cite
@article{arxiv.1310.3346,
title = {Multiplicity-free primitive ideals associated with rigid nilpotent orbits},
author = {Alexander Premet},
journal= {arXiv preprint arXiv:1310.3346},
year = {2014}
}
Comments
minor changes and corrections; the present version has been accepted for publication