# Springer fibers for the minimal and the minimal special nilpotent orbits

## TL;DR

This paper characterizes Springer fibers associated with minimal and minimal special nilpotent orbits in simple Lie algebras, providing insights into their structure and resolving a conjecture by Humphreys about related graphs.

## Contribution

It offers a detailed description of Springer fibers for specific nilpotent orbits and confirms Humphreys' conjecture on their associated graphs.

## Key findings

- Descriptions of Springer fibers for minimal and minimal special nilpotent orbits
- Resolution of Humphreys' conjecture on graphs attached to Springer fibers
- Enhanced understanding of the structure of Springer fibers in Lie theory

## Abstract

We describe Springer fibers corresponding to the minimal and minimal special nilpotent orbits of simple Lie algebras. As a result, we give an answer to the conjecture of Humphreys regarding some graphs attached to Springer fibers.