Topology of two-row Springer fibers for the even orthogonal and symplectic group
Topology of two-row Springer fibers for the even orthogonal and symplectic group
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偶正交辛群的两排 Springer 纤维的拓扑
DOI：
10.1090/s0002-9947-2017-07194-4
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Wilbert
中科院分区：
文献类型：
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作者：
A. Wilbert
我们为与偶正交群相关的每一个两行 Springer 纤维构建了一个显式拓扑模型（类似于 Khovanov 和 Russell 的工作中出现的拓扑 Springer 纤维），并证明各自的拓扑模型与其相应的 Springer 纤维是同胚的。这证实了 Ehrig 和 Stroppel 关于偶正交群的等排 Springer 纤维拓扑的猜想。此外，我们证明辛群的每一个两行 Springer 纤维与偶正交群的某个两行 Springer 纤维的连通分量是同构的（甚至作为代数簇同构）。
We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms a conjecture by Ehrig and Stroppel concerning the topology of the equal-row Springer fiber for the even orthogonal group. Moreover, we show that every two-row Springer fiber for the symplectic group is homeomorphic (even isomorphic as an algebraic variety) to a connected component of a certain two-row Springer fiber for the even orthogonal group.