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Pré-Publication, Document De Travail Année : 2010

Restriction to Levi subalgebras and generalization of the category O

Guillaume Tomasini
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Résumé

The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.
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hal-00523986 , version 1 (06-10-2010)

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Guillaume Tomasini. Restriction to Levi subalgebras and generalization of the category O. 2010. ⟨hal-00523986⟩

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