Topology of two-row Springer fibers for the even orthogonal and symplectic group

TL;DR

This paper constructs explicit topological models for two-row Springer fibers in the context of the even orthogonal and symplectic groups, confirming conjectures and establishing homeomorphisms with algebraic varieties.

Contribution

It provides explicit topological models for these Springer fibers and proves their homeomorphism to the algebraic varieties, confirming a conjecture by Ehrig and Stroppel.

Findings

Topological models are homeomorphic to Springer fibers.

Confirmed Ehrig and Stroppel's conjecture.

Symplectic two-row Springer fibers are homeomorphic to orthogonal ones.

Abstract

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms a conjecture by Ehrig and Stroppel concerning the topology of the equal-row Springer fiber for the even orthogonal group. Moreover, we show that every two-row Springer fiber for the symplectic group is homeomorphic (even isomorphic as an algebraic variety) to a connected component of a certain two-row Springer fiber for the even orthogonal group.