Components of Springer fibers associated to closed orbits for the symmetric pairs (Sp(2n),Sp(2p)×Sp(2q))(Sp(2n),Sp(2p)×Sp(2q)) and (SO(2n),GL(n))(SO(2n),GL(n)), II

This is the second of two articles that consider the pairs of complex reductive groups (G,K)=(Sp(2n),Sp(2p)×Sp(2q))(G,K)=(Sp(2n),Sp(2p)×Sp(2q)) and (SO(2n),GL(n))(SO(2n),GL(n)) and components of Springer fibers associated to closed K-orbits in the flag variety of G  . In the first an algorithm is given to compute the associated variety of any discrete series representation of GR=Sp(p,q)GR=Sp(p,q) and SO⁎(2n)SO⁎(2n) and to concretely describe the corresponding component of a Springer fiber. These results are used here to compute associated cycles of discrete series representations. For each Harish-Chandra cell containing a discrete series representation, a particular discrete series representation is identified for which the structure of the component is sufficiently simple that the multiplicity in the associated cycle can be calculated. Coherent continuation is then applied to compute associated cycles of all representations in such a cell.