论文标题
量子排列组
Quantum permutation groups
论文作者
论文摘要
排列组$ s_n $具有量子模拟$ s_n^+$，该$ n \ geq4 $是无限的。我们回顾了有关$ s_n^+$的已知事实，尤其是其简单性属性，weingarten cyculus和同构$ s_4^+= so_3^{ - 1} $及其后果。然后，我们讨论封闭子组的结构$ g \ subset s_n^+$，尤其是有限图的量子对称组$ g^+（x）\ subset s_n^+$，特别注意量子反射组$ h_n^{s+} $。我们还更加一般地讨论了有限量子空间$ z $的量子对称组$ s_z^+$及其封闭的子组$ g \ subset s_z^+$，特别注意量子图案例和量子反射组。
The permutation group $S_N$ has a quantum analogue $S_N^+$, which is infinite at $N\geq4$. We review the known facts regarding $S_N^+$, and notably its easiness property, Weingarten calculus, and the isomorphism $S_4^+=SO_3^{-1}$ and its consequences. We discuss then the structure of the closed subgroups $G\subset S_N^+$, and notably of the quantum symmetry groups of finite graphs $G^+(X)\subset S_N^+$, with particular attention to the quantum reflection groups $H_N^{s+}$. We also discuss, more generally, the quantum symmetry groups $S_Z^+$ of the finite quantum spaces $Z$, and their closed subgroups $G\subset S_Z^+$, with particular attention to the quantum graph case, and to quantum reflection groups.
