Springer correspondence for the split symmetric pair in type $A$
Springer correspondence for the split symmetric pair in type $A$
复制标题
DOI：
10.1112/s0010437x18007443
复制
发表时间：
2016-08
影响因子：
1.8
通讯作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
中科院分区：
文献类型：
--
作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
本文利用Fourier变换、抛物归纳函子和一个邻近的圈层构造方法建立了对称对$（SL（N），SO（N））$的Springer对应.作为结果的应用，我们看到Hessenberg簇的上同调可以用对称群的Hecke代数在q=-1 $的不可约表示来表示.相反，我们看到对称群的Hecke代数在q=-1 $的不可约表示在几何中出现。
In this paper we establish Springer correspondence for the symmetric pair $(\text{SL}(N),\text{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$ . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.