Tensor Product Categorifications and the Super Kazhdan–Lusztig Conjecture

Abstract

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie superalgebra gl n|m (C) as formulated originally by the first author. We also prove for the first time that any integral block of category O for gl n|m (C) (and also all of its parabolic analogs) possesses a graded version which is Koszul. Our approach depends crucially on an application of the uniqueness of tensor product categorifications established recently by the second two authors.