论文标题
交叉比对称性和Möbius结构方程
Symmetries of cross-ratios and the equation for Möbius structures
论文作者
论文摘要
我们考虑正交表示$η_n：s_n \ curvearrowright \ mathbb {r}^n $的对称组的$ s_n $，$ n \ ge 4 $，带有$ n = n！/8 $由交叉比例的对称性动机。对于$ n = 5 $，我们发现$η_5$的分解成不可约组件，并表明其中一个组件提供了方程的解决方案，这些方程描述了Sub-Möbius结构中的Möbius结构。从这个意义上讲，定义Möbius结构的条件已经隐藏在交叉比例的对称性中。
We consider orthogonal representations $η_n:S_n \curvearrowright \mathbb{R}^N$ of the symmetry groups $S_n$, $n\ge 4$, with $N=n!/8$ motivated by symmetries of cross-ratios. For $n=5$ we find the decomposition of $η_5$ into irreducible components and show that one of the components gives the solution to the equations, which describe Möbius structures in the class of sub-Möbius structures. In this sense, the condition defining Möbius structures is hidden already in symmetries of cross-ratios.
