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Article

Graded tensor product categorifications and the super Kazhdan-Lusztig conjecture

International Mathematical Research Notices. 2017. No. 20. P. 6329-6410.
Brundan J., Losev Ivan, Webster B.

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie super algebra 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.