Categorification of quantum symmetric pairs I

Abstract

We categorify a coideal subalgebra of the quantum group of ${\mathfrak{sl}}_{2r+1}$ by introducing a 2-category analogous to the one defined by Khovanov–Lauda–Rouquier, and show that self-dual indecomposable 1-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the category $\mathcal{O}$ of type B/C.