Aaron Lauda, USC

Title: Braiding in higher representation theory with applications to symmetric groups

Abstract: Since the pioneering work of Chuang and Rouquier, the construction of highly nontrivial derived equivalences has been one of the most powerful tools resulting from higher representation theory. Cautis-Kamnitzer-Licata showed that these derived equivalences arising from categorified quantum groups gave rise to categorical actions of braid groups of the corresponding Lie type. In 2011, motivated by the discovery of odd Khovanov homology, Ellis-Khovanov-L. proposed a new odd categorification of 𝔰𝔩₂. At the same time, this 'odd 𝔰𝔩₂' was independently discovered by Kang-Kashiwara-Tsuchioka, who investigated super categorifications of Kac-Moody algebras. In this talk, we will explain joint work with Mark Ebert and Laurent Vera, giving new super analogs of the derived equivalences studied by Chuang and Rouquier, coming from the odd categorification of 𝔰𝔩₂. Just as Chuang and Rouquier used their equivalences to achieve new results on the modular representation theory of the symmetric group, we will discuss how our new super equivalences can be applied to the spin symmetric group.