Orbital varieties in type $D$

We extend the results of [5] to type D, again correcting the proofs of these results in [4]. We first note that the hyperoctahedral Weyl group W ′ of type Bn acts by automorphisms on the semisimple Lie algebra g of type Dn, so that the orbital variety V (w) defined in [4] makes sense for any w ∈ W ; we say that w1,w2 ∈ W ′ lie in the same geometric cell if V (w1) = V (w2) . The classification theorem then applies to any w ∈ W ; recall that any such w has well-defined left and right domino tableaux TL(w),TR(w) of the same shape.