Cohomology-class expansion for Springer-fiber components

Determine how to expand the cohomology class of each irreducible component of a Springer fiber in the Schubert-class basis of the cohomology ring of the complete flag variety.

Background

For a partition lambda of n, the paper describes the Springer fiber associated with a nilpotent matrix of Jordan type lambda. Spaltenstein's results index its irreducible components by standard Young tableaux T, with the component denoted by mathcal B_T.

The paper notes that Springer posed the unresolved problem of expressing the cohomology class [mathcal B_T] in terms of Schubert classes. The paper addresses this only in the special case of Richardson tableaux, where the component is a Richardson variety and the expansion reduces to computing Schubert structure constants; it does not resolve the general problem.