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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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