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

@article{AIF_2000__50_2_537_0,
     author = {Mathieu, Olivier},
     title = {Classification of irreducible weight modules},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     pages = {537-592},
     doi = {10.5802/aif.1765},
     zbl = {0962.17002},
     mrnumber = {2001h:17017},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2000__50_2_537_0}
}
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. http://www.numdam.org/item/AIF_2000__50_2_537_0/

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