Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality

We describe how certain cyclotomic Nazarov–Wenzl algebras occur as endomorphism rings of projective modules in a parabolic version of BGG category O of type D. Furthermore we study a family of subalgebras of these endomorphism rings which exhibit similar behaviour to the family of Brauer algebras even when they are not semisimple. The translation functors on this parabolic category O are studied and proven to yield a categorification of a coideal subalgebra of the general linear Lie algebra. Finally this is put into the context of categorifying skew Howe duality for these subalgebras.