  We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_k
such that the category of finite dimensional \mathbb{D}_k-modules is equivalent
to the category of perverse sheaves on the isotropic Grassmannian of type D_k
constructible with respect to the Schubert stratification. The connection is
given by an explicit isomorphism to the endomorphism algebra of a projective
generator described in by Braden. The algebra is obtained by a "folding"
procedure from the generalized Khovanov arc algebras. We relate this algebra to
the category of finite dimensional representations of the orthosymplectic
supergroups. The proposed equivalence of categories gives a concrete
description of the categories of finite dimensional SOSP(m|2n)-modules.
