On the Fixed Points of Springer Varieties in Type A

Springer varieties are sub-varieties of the full (complete) flag variety Fℓn(C), which can be thought of as the fiber over X of the Springer resolution of singularities of cone of nilpotent endomorphism X : V −→ V, where X is a nilpotent endomorphism in its Jordan canonical form of type λ and V is a n−dimensional vector space over C (V = Cn for convenience). The geometry of Springer varieties is reviewed in this article, along with their Sk− fixed points. We accomplish this by briefly reviewing nilpotent orbits in type A within the framework of integer partition.