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

摘要

Let (G,K) be either (Sp(2n),GL(n)) or (O(n),O(p)×O(q)), p+q=n. This is the second of two articles describing the structure of certain components of Springer fibers related to the pair (G,K). The results of the first are used to show that certain components of Springer fibers are iterated bundles. Several consequences, including a vanishing theorem for sheaf cohomology, are given. It is shown that for (Sp(2n),GL(n)) a maximal torus of K acts on these components.