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Type A blocks of super category $$\mathcal{O}$$. (English) Zbl 1396.17005
It is known that the study of the BGG category $$\mathcal{O}$$ for the queer Lie superalgebra $$\mathfrak{q}_n$$ reduces to the study of three types of blocks, so called blocks of types $$A$$, $$B$$ and $$C$$. The paper under review studies blocks of type $$A$$ and establishes for them the truth of the Kazhdan-Lusztig conjecture as formulated by Cheng, Kwon and Wang. The authors use tools from higher representation theory to establish an equivalence of categories between the type $$A$$ blocks of $$\mathfrak{q}_n$$ and integral blocks of category $$\mathcal{O}$$ for a general linear Lie superalgebra. This reduces the original problem to the known case of general linear Lie superalgebras.

MSC:
 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B20 Simple, semisimple, reductive (super)algebras 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 18D99 Categorical structures
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References:
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