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Gelfand-Kirillov dimensions and annihilator varieties of highest weight modules of exceptional Lie algebras
Let $L(λ)$ be an irreducible highest weight module of a complex simple Lie algebra of exceptional type, with highest weight $λ-ρ$, where $ρ$ is half the sum of positive roots. Its annihilator variety is the closure of a nilpotent orbit of dimension twice the Gelfand--Kirillov (GK) dimension of $L(λ)
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