Irreducible components of two-row Springer fibers for all classical types

Abstract

We give an explicit description of the irreducible components of two-row Springer fibers for all classical types using cup diagrams. Cup diagrams can be used to label the irreducible components of two-row Springer fibers. We use these diagrams to explicitly write down relations between the vector spaces of the flags contained in a given irreducible component. This generalizes results by Stroppel–Webster and Fung for type A to all classical types.