  We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig
polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of
type $A_n$ and consequently an explicit counting formula for the dimension of
the morphism spaces between indecomposable projective objects in the
corresponding category $\O_0^\p$. As a byproduct we categorify irreducible
$W_n$-modules corresponding to pairs of one-line partitions. Finally we
indicate the motivation for introducing the combinatorics by connections to
Springer theory, the category of perverse sheaves on isotropic Grassmannians
and to Brauer algebras which will be treated in \cite{ES}.

Representation Theory;Combinatorics