On the Fixed Points of Springer Varieties in Type A

Abstract

Springer varieties are sub-varieties of the full (complete) flag variety Fℓn(C)Fℓn​(C), which can be thought of as the fiber over XX of the Springer resolution of singularities of the cone of nilpotent endomorphisms X:V⟶VX:V⟶V, where XX is a nilpotent endomorphism in its Jordan canonical form of type λλ and VV is an nn-dimensional vector space over CC (V=CnV=Cn for convenience). The geometry of Springer varieties is reviewed in this article, along with their SkSk-fixed points. We accomplish this by briefly reviewing nilpotent orbits in type AA within the framework of integer partitions.