Infinitesimal Blaschke conjectures on projective spaces

Chiaki Tsukamoto

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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 $M = \oplus_{λ} M_{λ}$ , 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 $𝒪$ .