有限群的Clifford周期性
Clifford Periodicity from Finite Groups
摘要：
从由Gamma矩阵生成的有限Clifford群的简单组合性质出发，推导出正交群$O(n)$的$Pin$和$Spin$表示的周期δ.我们还包括任意签名$O(p,q)$的情况。表示类型的变化可以看作是复平面中的旋转。基本结果是，添加$(+)$维在逆时针方向上执行$π/4$的旋转，但是对于度量中的每个$(-)$符号，旋转是顺时针的。
英文摘要：
We deduce the periodicity 8 for the type of $Pin$ and $Spin$ representations of the orthogonal groups $O(n)$ from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of arbitrary signature $O(p,q)$. The changes in the type of representation can be seen as a rotation in the complex plane. The essential result is that adding a $(+)$ dimension performs a rotation by $π/4$ in the counter clock-wise sense, but for each $(-)$ sign in the metric, the rotation is clockwise.
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