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The Annihilation theorem for the completely reducible Lie superalgebras

Maria Gorelik·Emmanuel Lanzmann
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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 $\osp(1,2l)$-Verma module for its annihilator to be generated by its intersection with the centre. This answers a question of Musson.

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BibTeXRIS

Maria Gorelik, Emmanuel Lanzmann. 1999-04-07. The Annihilation theorem for the completely reducible Lie superalgebras. https://doi.org/10.1007/s002220050338

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