论文标题
对Kostant的凸定理的几何形状
A geometric take on Kostant's Convexity Theorem
论文作者
论文摘要
鉴于一个紧凑的谎言组$ g $和一个正交$ g $ - 代表$ v $，我们为Orbit Space $ v/g $的封闭子集提供了一个纯度标准，以$ v $中的凸面前图。实际上，这也与自然商映射$ v \ to v/g $相结合，被任意子标准$ v \替换为x $。 在这种情况下，我们介绍了“脂肪部分”的概念，该概念概括了极性表示，非平凡的共光的表示和等含量叶。 我们表明，Kostant的凸定理部分从极地表示将其概括为带有脂肪部分的子宫，并举例说明它并未完全概括为这种情况。
Given a compact Lie group $G$ and an orthogonal $G$-representation $V$, we give a purely metric criterion for a closed subset of the orbit space $V/G$ to have convex pre-image in $V$. In fact, this also holds with the natural quotient map $V\to V/G$ replaced with an arbitrary submetry $V\to X$. In this context, we introduce a notion of "fat section" which generalizes polar representations, representations of non-trivial copolarity, and isoparametric foliations. We show that Kostant's Convexity Theorem partially generalizes from polar representations to submetries with a fat section, and give examples illustrating that it does not fully generalize to this situation.
