Type C blocks of super category $$\mathcal {O}$$

Abstract

We show that the blocks of category $$\mathcal {O}$$ for the Lie superalgebra $${\mathfrak {q}}_n({\mathbb {C}})$$ associated to half-integral weights carry the structure of a tensor product categorification for the infinite rank Kac-Moody algebra of type $$\hbox {C}_\infty $$ . This allows us to prove two conjectures formulated by Cheng, Kwon and Wang. 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.