追踪量子置换群的轨道
Tracing the orbitals of the quantum permutation group
AI总结：
本文通过非交换平坦矩阵模型证明量子置换群具有自由轨道，并给出中间量子子群及量子置换群上四次单项式Haar态的显式公式。
摘要：
利用一个适当的非交换平坦矩阵模型，证明了量子置换群具有自由轨道：即，函数代数生成元中的单项式仅因平凡原因才可能为零。证明了在经典置换群与量子置换群之间的任何严格中间量子子群必须具有自由的三轨道。这被用于给出四次单项式上 Haar 态的显式公式，这些公式对这样的中间量子子群以及量子置换群本身均成立。
英文摘要：
Using a suitably noncommutative flat matrix model, it is shown that the quantum permutation group has free orbitals: that is, a monomial in the generators of the algebra of functions can be zero for trivial reasons only. It is shown that any strictly intermediate quantum subgroup between the classical and quantum permutation groups must have free three-orbitals. This is used to give explicit formulae for the Haar state on degree four monomials that hold for such intermediate quantum subgroups as well as the quantum permutation group itself.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
