论文标题
关于git商和真实形式
On GIT quotients and real forms
论文作者
论文摘要
我们考虑复杂代数组的复杂代数$ \ MATHBF {G} $的动作，来自$ \ m arterbf {g} $ of $ g $ of $ \ mathbf {g} $和$ x $的$ \ mathbf {x} $的真实形式$ g $的动作。我们探索复杂git商的真实点$ \ mathbf {x / \！\！\！ / g} $与真实的git商$ x / \！\！ / g $由Richardson和Slodowy定义的。我们证明，可以将$ \ mathbf {x / \！\！ / g} $的某种真实点提升为$ x / \！\！ / g $的商，也许是在更改真实形式后，我们将可能的升降机数链接到同胞集。然后，我们将结果应用于字符品种，并研究$ \ mathrm {sl} _3（\ Mathbb {C}）$的特定情况 - $ \ Mathbb {z} $的字符品种。
We consider actions of complex algebraic groups $\mathbf{G}$ on complex algebraic varieties $\mathbf{X}$, coming from actions of real forms $G$ of $\mathbf{G}$ and $X$ of $\mathbf{X}$. We explore the links between the real points of the complex GIT quotient $\mathbf{X /\!\!/ G}$ and the real GIT quotient $X /\!\!/ G$ defined by Richardson and Slodowy. We prove that some type of real points of $\mathbf{X /\!\!/ G}$ can be lifted to a quotient of the form $X /\!\!/ G$ maybe after changing the real forms, and we link the number of possible lifts to a co-homology set. We apply then the results to character varieties, and study the particular case of the $\mathrm{SL}_3(\mathbb{C})$-character variety for $\mathbb{Z}$.
