A generalization of the category $ \mathcal{O}$ of Bernstein–Gelfand–Gelfand

Tomasini, Guillaume

doi:10.1016/j.crma.2010.03.008

Lie Algebras

A generalization of the category

O

of Bernstein–Gelfand–Gelfand
[Une généralisation de la catégorie

O

de Bernstein–Gelfand–Gelfand]

Présenté par : Michel Duflo

Tomasini, Guillaume ¹

¹ IRMA, CNRS et Université de Strasbourg, 7, rue René-Descartes, 67084 Strasbourg cedex, France

Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 509-512.

Résumé
Abstract

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.

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.

Reçu le : 2009-12-16
Accepté le : 2010-03-12
Publié le : 2010-03-29

DOI : 10.1016/j.crma.2010.03.008

Affiliations des auteurs :

Tomasini, Guillaume ¹

¹ IRMA, CNRS et Université de Strasbourg, 7, rue René-Descartes, 67084 Strasbourg cedex, France

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Tomasini, Guillaume. A generalization of the category $ \mathcal{O}$ of Bernstein–Gelfand–Gelfand. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 509-512. doi : 10.1016/j.crma.2010.03.008. http://www.numdam.org/articles/10.1016/j.crma.2010.03.008/

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