In the framework of canonical and dual canonical bases of Fock spaces, Brundan in 2003 formulated a Kazhdan–Lusztig-type conjecture for the characters of the irreducible and tilting modules in the Bernstein–Gelfand–Gelfand category for the general linear Lie superalgebra for the first time. In this paper, we prove Brundan’s conjecture and its variants associated to all Borel subalgebras in full generality.
"The Brundan–Kazhdan–Lusztig conjecture for general linear Lie superalgebras." Duke Math. J. 164 (4) 617 - 695, 15 March 2015. https://doi.org/10.1215/00127094-2881265