The Nil-Brauer Category - Categorification and Applications

Explore a 54-minute lecture on "The nil-Brauer category" presented by Jonathan Brundan from the University of Oregon at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Delve into the intricacies of this non-symmetric k-linear monoidal category, which serves as a nil version of the affine Brauer category. Discover how the nil-Brauer category categorifies the split ι-quantum group of rank one, as defined by Letzter, Kolb, and Bao-Wang. Examine two natural occurrences of the nil-Brauer category: one involving the Lauda-Rouquier categorification of sl_2, and another relating to singular Soergel bimodules associated with maximally isotropic Grassmannians in type D. Gain insights from Brundan's collaborative work with Weiqiang Wang, Ben Webster, Elijah Bodish, and Ben Elias in this advanced mathematical exploration recorded on January 12, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.