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This is a Quantitative Study study.

October 20, 2025Open Access

Weight modules and gluing of sheaves on the flag variety

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The derived version of the category is Koszul dual to the Kazhdan-Laumon Category O, establishing a deep link between algebraic structures and geometric interpretations.
A geometric realization of the weight modules is presented through unipotently monodromic sheaves on the flag variety, satisfying a singular support condition.
These results reveal new insights into classical constructions of weight modules over semisimple Lie algebras and their algebraic contexts.
The proposed Koszul duality connects the small quantum group to the semi-infinite flag variety through the geometry of affine Springer fibers.

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This study reveals the relationship between weight modules and sheaves on the flag variety, suggesting a new approach to Koszul duality.

Álvarez et al. (2025) studied this question.

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