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

TL;DR

This paper provides an explicit combinatorial description of the irreducible components of two-row Springer fibers across all classical types, extending previous results and utilizing cup diagrams for labeling and construction.

Contribution

It introduces a unified method using cup diagrams to explicitly describe all irreducible components of two-row Springer fibers for all classical types, generalizing prior work.

Findings

Cup diagrams label irreducible components

Explicit description of flags in each component

Generalization to 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. Given a cup diagram, we explicitly write down all flags contained in the component associated to the cup diagram. This generalizes results by Stroppel--Webster and Fung to all classical types.