Hessenberg varieties, intersections of quadrics, and the Springer correspondence
Hessenberg varieties, intersections of quadrics, and the Springer correspondence
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DOI：
10.1090/tran/7934
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
中科院分区：
文献类型：
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作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
本文引入了一类由对称空间的Springer理论所产生的Hessenberg簇族。我们研究这些海森伯格品种的几何形状，并调查他们的单值表示详细使用的几何完全相交的二次曲面。我们得到分解这些monodromy表示成不可约的，并计算与这些不可约表示的IC复合物的傅立叶变换。本文的结果改进了[CVX]中关于分裂对称对（SL（N），SO（N））的Springer对应.
In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail using the geometry of complete intersections of quadrics. We obtain decompositions of these monodromy representations into irreducibles and compute the Fourier transforms of the IC complexes associated to these irreducible representations. The results of the paper refine (part of) the Springer correspondece for the split symmetric pair (SL(N),SO(N)) in [CVX2].