The torus equivariant cohomology rings of Springer varieties

Abstract

The Springer variety of type $A$ associated to a nilpotent operator on ${\mathbb{C}}^n$ in Jordan canonical form admits a natural action of the $\ell$-dimensional torus $T^{\ell }$ where $\ell$ is the number of the Jordan blocks. We give a presentation of the $T^{\ell }$-equivariant cohomology ring of the Springer variety through an explicit construction of an action of the $n$-th symmetric group on the $T^{\ell }$-equivariant cohomology group. The $T^{\ell }$-equivariant analogue of so called Tanisaki's ideal will appear in the presentation.

arXiv comment14 pages

References in corpus (2)

• The cohomology ring of the GKM graph of a flag manifold of classical type
• The equivariant cohomology rings of Peterson varieties

Cited by in corpus (2)

• The equivariant cohomology rings of regular nilpotent Hessenberg varieties in Lie type A: a research announcement
• Torus actions, localization and induced representations on cohomology