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Classification of irreducible weight modules

Olivier Mathieu — 2000

Annales de l'institut Fourier

Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤 -module M is called a 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 .

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