Primitive ideals, twisting functors and star actions for classical Lie superalgebras
K Coulembier, V Mazorchuk - Journal für die reine und angewandte …, 2016 - degruyter.com
K Coulembier, V Mazorchuk
Journal für die reine und angewandte Mathematik, 2016•degruyter.comWe study three related topics in representation theory of classical Lie superalgebras. The
first one is classification of primitive ideals, ie 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.
first one is classification of primitive ideals, ie 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.
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 . 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.
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