Δ-filtered modules and nilpotent orbits of a parabolic subgroup in

We study certain Δ-filtered modules for the Auslander algebra of k[T]/Tn⋊C2 where C2 is the cyclic group of order two. The motivation of this lies in the problem of describing the P-orbit structure for the action of a parabolic subgroup P of an orthogonal group. For any parabolic subgroup of an orthogonal group we construct a map from parabolic orbits to Δ-filtered modules and show that in the case of the Richardson orbit, the resulting module has no self-extensions.