Geometric properties of Springer fibers of type A over a division ring

Abstract

We define and study Springer fibers over a general division ring R over ℝ, rather than the usual algebraically closed field. We give examples of such Springer fibers and provide geometric properties, mostly about their irreducible components, that generalize properties known for Springer fibers over algebraically closed fields. In particular, when discussing the geometric properties of such Springer fibers, we focus on type A Springer fibers, that is, where the underlying Lie algebra is of type A.