An efficient algorithm computes gelfand-kirillov dimensions and determines annihilator varieties of highest weight modules.
In this paper, we give an efficient algorithm to compute the Gelfand-Kirillov dimensions of simple highest weight modules of exceptional Lie algebras. By using the Sommers-Achar duality, we also determine the annihilator varieties of these highest weight modules.
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Bai et al. (2025) studied this question.
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