Springer representations on the Khovanov Springer varieties

Geometry and cohomology of Khovanov-Springer varieties

The Khovanov-Springer variety X(n) is a certain subvariety of the variety of flags of length 2n, which has been studied from various different points of view. We give a new proof of the ring structure of the cohomology of X(n) and relate it to some interesting geometric, combinatorial and algebraic phenomena.

The torus equivariant cohomology rings of Springer varieties

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.

The $S^1$-equivariant cohomology rings of $(n-k,k)$ Springer varieties

The main result of this note gives an explicit presentation of the $S^1$-equivariant cohomology ring of the $(n-k,k)$ Springer variety (in type $A$) as a quotient of a polynomial ring by an ideal $I$, in the spirit of the well-known Borel presentation of the cohomology of the flag variety.

Springer 簇的 K-理论

K-theory of Springer varieties

本文以生成元与关系刻画 A 型 Springer 簇的拓扑 K-环，并将其与 Tanisaki 的整上同调环及 Abe、Horiguchi 的等变结果相对应。

Springer 簇的等变 $K$-理论

Equivariant $K$-theory of Springer Varieties

本文用生成元和关系描述了与幂零算子关联的 $A$ 型 Springer 簇 $\mathcal{F}_λ$ 的拓扑等变 $K$-环，平行并推广了已有的等变上同调环和普通拓扑 $K$-环的描述。

Poset pinball, GKM-compatible subspaces, and Hessenberg varieties

This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compatible subspace of an ambient GKM space. We also discuss poset-upper-triangularity, a key combinatorial notion in both GKM theory and more generally in localization theory in equivariant cohomology. With a view toward other applications, we present parts of our setup in a general algebraic and combinatorial framework. Second, motivated by our central problem o…