no. 2
Classification of irreducible weight modules
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 537-592

Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤-module M is called a weighted module if and only if M=⊕ λ M λ , where each weight space M λ is finite dimensional. The main result of the paper is the classification of all simple weight 𝔤-modules. Further, we show that their characters can be deduced from characters of simple modules in category 𝒪.

Soit 𝔤 une algèbre de Lie réductive et soit 𝔥 une sous-algèbre de Cartan. Un 𝔤-module M est dit module de poids si et seulement si il admet une décomposition M=⊕ λ M λ , où chaque espace de poids M λ est de dimension finie. Notre résultat principal est la classification de tous les 𝔤-modules de poids simples. Également, leurs caractères sont déduits de formules des caractères des modules simples de la catégorie 𝒪.

Mathieu, Olivier. Classification of irreducible weight modules. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 537-592. doi: 10.5802/aif.1765
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