Réduction de produits semi-directs et conjecture de Gel'fand et Kirillov
Relation between invertibility of Casimir operators and semisimplicity of quadratic Lie superalgebras.
Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules
In this article, we study the structure of Fock modules over super Virasoro algebras. As an application, we construct Bechi-Rouet–Stora–Tyutin type resolutions for super minimal models and their descendants.
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Représentations des algèbres de Lie résolubles
Représentations des groupes de Lie nilpotents
Representations of codimension one non-abelian nilradical Lie algebras.
Representations of solvable Lie algebras. II. Twisted group rings
Representations of the Lie ring over the ring of integers.
Restriction to Levi subalgebras and generalization of the category
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.
Rigidity of generalized Verma modules
We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).