Restriction to Levi subalgebras and generalization of the category O

Details Restriction to Levi subalgebras and generalization of the category O Restriction to Levi subalgebras and generalization of the category O

2010-10-07

arxiv.org/abs/1010.1347v1

Mathematics

Representation Theory

43 pages

Scientific paper

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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