Categorification of quantum symmetric pairs I
We categorify a coideal subalgebra of the quantum group of \mathfrak{sl}_{2r+1} by introducing a $2$ category a la 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 BGG category \mathcal{O} of type B/C.