论文标题
关于Hessenberg品种的T-量相结合的共同学
On the T-equivariant cohomology of Hessenberg varieties
论文作者
论文摘要
对于内态$ s：v \ rightArrow v $，有限维数复合矢量空间和完整标志品种上的圆环$ t $的动作$ \ text {gl} _n（{\ mathbb c}）/b $，我们对$ s $ is s $ is semisimple或常规nililpottent进行了描述。我们还计算了Hessenberg subvariety $ \ text {hes}（s，h）\ subseteq \ text {gl} _n（{\ mathbb c}）/b $的Hessenberg函数$ h $ h $ h $。对于一维圆环$ s $的动作和常规的nilpotent内态$ n：v \ rightarrow v $，我们为使用确定性的任何Hessenberg功能提供了新的Hessenberg品种$ \ text {Hes}（hs，h）$的赫森伯格品种$ \ text {hes h）$的新计算。
For an endomorphism $s:V\rightarrow V$ of a finite dimensional complex vector space and an action of a torus $T$ on the full flag variety $\text{GL}_n({\mathbb C})/B$, we give a description of its fixed point set when $s$ is semisimple or regular nilpotent. We also compute the one dimensional orbits of this action on the Hessenberg subvariety $\text{Hes}(s,h)\subseteq \text{GL}_n({\mathbb C})/B$ for any Hessenberg function $h$. For the action of the one dimensional torus $S$ and a regular nilpotent endomorphism $N:V\rightarrow V$, we give a new computation of the equivariant cohomology of the Hessenberg variety $\text{Hes}(N,h)$ for any Hessenberg function using determinantal conditions.
