论文标题
正交组的旋转表示
Spinorial Representations of Orthogonal Groups
论文作者
论文摘要
令$ g $为一个真正的紧凑型谎言组，这样$ g = g^0 \ rtimes c_2 $，$ g^0 $简单。这里$ g^0 $是包含身份的$ g $的连接组件，$ c_2 $是订单$ 2 $的环状组。我们给出了一个标准，即是否是正交表示$π：g \ to \ mathrm {o}（v）$提升到$ \ mathrm {pin}（v）$的最高权重$π$。我们还计算正交群体表示的第一和第二Stiefel-Whitney类。
Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, with $G^0$ simple. Here $G^0$ is the connected component of $G$ containing the identity and $C_2$ is the cyclic group of order $2$. We give a criterion for whether an orthogonal representation $π: G \to \mathrm{O}(V)$ lifts to $\mathrm{Pin}(V)$ in terms of the highest weights of $π$. We also calculate the first and second Stiefel-Whitney classes of the representations of the Orthogonal groups.
