We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng and Lam. We do this by establishing a new uniqueness theorem for tensor product categorifications motivated by work of Brundan, Losev, and Webster. Moreover we show that these BGG categories have Koszul graded lifts and super duality can be lifted to a graded equivalence.

中文翻译：

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一般线性李超代数的梯度超对偶

我们提供了新的证明，由Cheng和Wang猜想并由Cheng和Lam首次证明的一般线性Lie（超）代数的无限秩抛物BGG类之间的超对等性。为此，我们通过建立由Brundan，Losev和Webster推动的张量积分类的新唯一性定理。此外，我们证明了这些BGG类别具有Koszul分级提升，并且可以将超级对偶提升为分级对等。