实矩阵和对称矩阵

IF 2.3 1区 数学 Q1 MATHEMATICS
Tsao-Hsien Chen, D. Nadler
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引用次数: 0

摘要

我们构造了具有实特征值的$n×n$实矩阵的空间和具有实特征量的$n次n$对称矩阵的空间之间的分层同胚,它限制了单个$GL_n(\mathbb R)$-伴随轨道和$O_n(\mathbbC)$-伴轨道之间的实解析同构。在经典型李代数和箭袋变种李代数的更一般的设置中,我们也建立了类似的结果。为此,我们证明了线性空间的超Kahler商上对合的一个一般结果。我们讨论了(广义)Kostant-Sekiguchi对应关系的应用,实和对称伴随轨道闭包的奇点,以及实群和对称空间的Springer理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Real and symmetric matrices
We construct a stratified homeomorphism between the space of $n\times n$ real matrices with real eigenvalues and the space of $n\times n$ symmetric matrices with real eigenvalues, which restricts to a real analytic isomorphism between individual $GL_n(\mathbb R)$-adjoint orbits and $O_n(\mathbb C)$-adjoint orbits. We also establish similar results in more general settings of Lie algebras of classical types and quiver varieties. To this end, we prove a general result about involutions on hyper-Kahler quotients of linear spaces. We discuss applications to the (generalized) Kostant-Sekiguchi correspondence, singularities of real and symmetric adjoint orbit closures, and Springer theory for real groups and symmetric spaces.
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来源期刊
CiteScore
3.40
自引率
0.00%
发文量
61
审稿时长
6-12 weeks
期刊介绍: Information not localized
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