Rational actions associated to the adjoint representation
Recent advances in enveloping algebras of semi-simple Lie-algebras
Réduction de produits semi-directs et conjecture de Gel'fand et Kirillov
Représentations des algèbres de Lie résolubles
Representations of Coxeter Groups and Hecke Algebras.
Representations of solvable Lie algebras. II. Twisted group rings
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).