Seminar

In the early 2000s, Chuang and Rouquier initiated a systematic study of $\mathfrak{sl}_2$-categorification, leading to a proof of Brou\'e's Abelian defect conjecture for the symmetric group. This work inspired a more general framework for categorifications of representations of Kac-Moody algebras, and led to the discovery of the remarkable quiver Hecke algebras. In this talk, I will discuss some work extending this theory to the context of superalgebra. Of central importance is the odd nil Hecke algebra of Ellis-Khovanov-Lauda and the more general the odd quiver Hecke algebras of Kang-Kashiwara-Tsuchioka, as well as cyclotomic quotients of these algebras.  I will motivate the discussion with two examples, the twisted group algebra of the symmetric group, and category O for the Lie superalgebra $\mathfrak{q}_n$.