Tensor product categorifications and the super Kazhdan-Lusztig conjecture

By Jonathan Brundan, I. Losev, Ben Webster. 2013

70 citations recorded by the source corpus.

We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie super algebra $\mathfrak{gl}_{n|m}(\mathbb{C})$ as formulated originally by the first author. We also prove for the first time that any integral block of category O for $\mathfrak{gl}_{n|m}(\mathbb{C})$ (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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dde11b07da15981c894ca15290fa695475c67c73