Divided Difference Operator for the Highest root Hessenberg variety

Hessenberg表示的有限差分算子

Divided difference operators for Hessenberg representations

本文针对A型正则半单Hessenberg簇等变上同调环的对称群扭曲表示，利用有限差分算子将其分解为子表示直和，范畴化了色拟对称函数间的模关系。

Poset pinball, highest forms, and (n-2,2) Springer varieties

We study type $A$ nilpotent Hessenberg varieties equipped with a natural $S^1$-action using techniques introduced by Tymoczko, Harada-Tymoczko, and Bayegan-Harada, with a particular emphasis on a special class of nilpotent Springer varieties corresponding to the partition $λ= (n-2,2)$ for $n \geq 4$. First we define the adjacent-pair matrix corresponding to any filling of a Young diagram with $n$ boxes with the alphabet $\{1,2,\ldots,n\}$. Using the adjacent-pair matrix we make more explicit and also extend some statements concerning highest forms of linear operators in previous work of Tymocz…

Divided difference operators for partial flag varieties

Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the equivariant cohomology of G/P for arbitrary partial flag varieties of arbitrary Lie type, and show how to use them in the ordinary cohomology of G/P. We provide three applications. The first shows that all Schubert classes of partial flag varieties can be generated from a sequence of divided difference operators on the highest-degree Schubert class. The second…