The Annihilation theorem for the completely reducible Lie superalgebras
Abstract
A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1,2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not generated by its intersection with the centre of universal enveloping algebra. More generally, Musson produced in [Mu1] a family of such "singular" Verma modules for osp(1,2l) cases. In this article we give a necessary and sufficient condition on the highest weight of a -Verma module for its annihilator to be generated by its intersection with the centre. This answers a question of Musson.
Cite
@article{arxiv.math/9904030,
title = {The Annihilation theorem for the completely reducible Lie superalgebras},
author = {Maria Gorelik and Emmanuel Lanzmann},
journal= {arXiv preprint arXiv:math/9904030},
year = {2009}
}
Comments
28 pages, to appear in Inventiones mathematicae