Type A blocks of super category O
Jonathan Brundan, Nicholas Davidson

TL;DR
This paper proves an equivalence between blocks of category O for general linear and queer Lie superalgebras, confirming the Kazhdan-Lusztig conjecture for type A blocks in the queer case.
Contribution
It establishes a new equivalence of categories that confirms the Kazhdan-Lusztig conjecture for type A blocks of the queer Lie superalgebra.
Findings
Equivalence of blocks between general linear and queer Lie superalgebras
Validation of Kazhdan-Lusztig conjecture for type A blocks in queer Lie superalgebra
Implication for representation theory of Lie superalgebras
Abstract
We show that every integral block of category O for the general linear Lie superalgebra is equivalent to a corresponding block of category O for the queer Lie superalgebra. This implies the truth of the Kazhdan-Lusztig conjecture for the so-called type A blocks of category O for the queer Lie superalgebra, as formulated by Cheng, Kwon and Wang.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
