Type A blocks of super category O

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.