Betti numbers of Springer fibers in type A

TL;DR

This paper computes the Betti numbers of Springer fibers in type A by constructing a cell decomposition based on an analogue of Coxeter length, facilitating explicit topological calculations.

Contribution

It introduces a novel cell decomposition for Springer fibers in type A, enabling precise Betti number calculations.

Findings

Betti numbers of Springer fibers in type A are explicitly determined.

A new cell decomposition method is developed based on Coxeter length.

The approach simplifies topological analysis of Springer fibers.

Abstract

We determine the Betti numbers of the Springer fibers in type A. To do this, we construct a cell decomposition of the Springer fibers. The codimension of the cells is given by an analogue of the Coxeter length. This makes our cell decomposition well suited for the calculation of Betti numbers.