论文标题
仿射球形品种的根子组
Root subgroups on affine spherical varieties
论文作者
论文摘要
鉴于连接的还原代数组$ g $和一个Borel子组$ b \ subseteq g $，我们研究了$ b $ normalistalized的单参数添加剂组对仿射球形球形$ g $ varieties。我们建立了此类动作及其权重的基本特性，并讨论了许多展示各种特征的例子。我们提出了这样的行动的结构，该动作概括了众所周知的一参参数添加剂对仿生孢子品种的构造。 Using this construction, for every affine horospherical $G$-variety $X$ we obtain a complete description of all $G$-normalized one-parameter additive group actions on $X$ and show that the open $G$-orbit in $X$ can be connected with every $G$-stable prime divisor via a suitable choice of a $B$-normalized one-parameter additive group action.最后，当$ g $是半完整排名$ 1 $的$ g $时，我们可以完全描述所有$ b $ normalized的单参数添加性集体动作，以仿射球形$ g $ g $ -varieties具有最大圆环$ t \ subseteq b $的开放式轨道。
Given a connected reductive algebraic group $G$ and a Borel subgroup $B \subseteq G$, we study $B$-normalized one-parameter additive group actions on affine spherical $G$-varieties. We establish basic properties of such actions and their weights and discuss many examples exhibiting various features. We propose a construction of such actions that generalizes the well-known construction of normalized one-parameter additive group actions on affine toric varieties. Using this construction, for every affine horospherical $G$-variety $X$ we obtain a complete description of all $G$-normalized one-parameter additive group actions on $X$ and show that the open $G$-orbit in $X$ can be connected with every $G$-stable prime divisor via a suitable choice of a $B$-normalized one-parameter additive group action. Finally, when $G$ is of semisimple rank $1$, we obtain a complete description of all $B$-normalized one-parameter additive group actions on affine spherical $G$-varieties having an open orbit of a maximal torus $T \subseteq B$.
