REAL DOUBLE COSET SPACES AND THEIR INVARIANTS
REAL DOUBLE COSET SPACES AND THEIR INVARIANTS
复制标题
实双陪集空间及其不变量
DOI：
10.1016/j.jalgebra.2009.01.028
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Gerald W. Schwarz
中科院分区：
文献类型：
--
作者：
A. Helminck;Gerald W. Schwarz
设G是复约化群的真实的形式.设给定G的对合σ和θ.设H=Gσ表示σ的不动群，K=Gθ表示θ的不动群.我们对计算双陪集空间H\G/K感兴趣。我们使用矩映射和不变量理论的技术来计算双陪集，特别是那些封闭的。我们的结果的一个突出点是一个分层的商的紧凑环面上的封闭的双陪集纤维作为一个集合的平凡丛。
Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H=Gσdenote the fixed group of σ and let K=Gθdenote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our results is a stratification of a quotient of a compact torus over which the closed double cosets fiber as a collection of trivial bundles.