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Primitive ideals, twisting functors and star actions for classical Lie superalgebras

  • Kevin Coulembier EMAIL logo and Volodymyr Mazorchuk

Abstract

We study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category 𝒪. The third topic addresses deformed orbits of the Weyl group. These take over the role of the usual Weyl group orbits for Lie algebras, in the study of primitive ideals and twisting functors for Lie superalgebras.

Funding statement: Kevin Coulembier is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO). Volodymyr Mazorchuk is partially supported by the Swedish Research Council.

Acknowledgements

We thank Ian Musson and Jens Carsten Jantzen for useful discussions.

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Received: 2014-01-27
Revised: 2014-04-09
Published Online: 2014-10-01
Published in Print: 2016-09-01

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