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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 509-512 (mai 2010)
Doi : 10.1016/j.crma.2010.03.008
Received : 16 December 2009 ;  accepted : 12 Mars 2010
A generalization of the category   of Bernstein–Gelfand–Gelfand
Une généralisation de la catégorie   de Bernstein–Gelfand–Gelfand
 

Guillaume Tomasini
IRMA, CNRS et Université de Strasbourg, 7, rue René-Descartes, 67084 Strasbourg cedex, France 

Abstract

In the study of simple modules over a simple complex Lie algebra, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this note, we define a family of categories which generalizes the BGG category. We classify the simple modules for some of these categories. As a consequence we show that these categories are semisimple.

The full text of this article is available in PDF format.
Résumé

L’étude des représentations irréductibles d’une algèbre de Lie simple définie sur le corps des nombres complexes a conduit Bernstein, Gelfand et Gelfand a introduire une catégorie qui fournit un cadre naturel pour les modules de plus haut poids. Le but de cette note est de présenter une construction d’une famille de catégories généralisant celle de Bernstein–Gelfand–Gelfand. Nous décrivons les modules simples de certaines de ces catégories. Cette classification permet de montrer que ces catégories sont semi-simples.

The full text of this article is available in PDF format.


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