The partial compactification of the universal centralizer
The partial compactification of the universal centralizer
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DOI：
10.1007/s00029-023-00873-8
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发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
Ana Bălibanu
中科院分区：
文献类型：
--
作者：
Ana Bălibanu
半简单代数群的普适中心子是正则元的中心子族，由它们的共轭类参数化。当群为伴随型时，通过取奇异紧化中各纤维的闭包，构造了万向扶正器的光滑对数辛纤维紧化。我们利用奇异紧化的几何学给出了它的辛叶的明确描述。我们还证明了紧化扶正器纤维与某些Hessenberg簇是同构的——我们应用这一联系计算了部分紧化的奇异上同调，并研究了相应的普适Hessenberg簇的几何。
The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise compactification of the universal centralizer by taking the closure of each fiber in the wonderful compactification. We use the geometry of the wonderful compactification to give an explicit description of its symplectic leaves. We also show that the compactified centralizer fibers are isomorphic to certain Hessenberg varieties -- we apply this connection to compute the singular cohomology of the partial compactification, and to study the geometry of the corresponding universal Hessenberg family.