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We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_ksuch that the category of finite dimensional \mathbb{D}_k-modules is equivalentto the category of perverse sheaves on the isotropic Grassmannian of type D_kconstructible with respect to the Schubert stratification. The connection isgiven by an explicit isomorphism to the endomorphism algebra of a projectivegenerator described in by Braden. The algebra is obtained by a "folding"procedure from the generalized Khovanov arc algebras. We relate this algebra tothe category of finite dimensional representations of the orthosymplecticsupergroups. The proposed equivalence of categories gives a concretedescription of the categories of finite dimensional SOSP(m|2n)-modules.

Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)