The Torus-Equivariant Cohomology of Nilpotent Orbits

TL;DR

This paper computes the equivariant cohomology of regular and minimal nilpotent orbits in complex simple Lie algebras, revealing their geometric and topological properties under torus actions.

Contribution

It provides explicit calculations of the torus-equivariant cohomology for key nilpotent orbits, advancing understanding of their geometric structure.

Findings

Explicit equivariant cohomology of regular nilpotent orbit

Explicit equivariant cohomology of minimal nilpotent orbit

Insights into the topology of nilpotent orbits under torus actions

Abstract

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the action of a maximal compact torus of the overall group in question.