∆-filtered modules and nilpotent orbits of a parabolic subgroup in ON

We study certain ∆-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 ∆-filtered modules and show that in the case of the Richardson orbit, the resulting module has no self-extensions.