Type C blocks of super category O

Abstract

We show that the blocks of category O for the Lie superalgebra q_n associated to half-integral weights carry the structure of a tensor product categorification for the infinite rank Kac-Moody algebra of type C. This allows us to prove two conjectures formulated by Cheng, Kwon and Lam. We then focus on the full subcategory consisting of finite-dimensional representations, which we show is a highest weight category with blocks that are Morita equivalent to certain generalized Khovanov arc algebras.

32 pages

References in corpus (1)

• 2-Kac-Moody algebras

Cited by in corpus (2)

• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebras $D(2|1;\zeta )$
• A proof of Comes-Kujawa's conjecture