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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2012.10975 |
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| _version_ | 1866917743143419904 |
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| author | Banica, Teo |
| author_facet | Banica, Teo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_10975 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantum permutation groups Banica, Teo Quantum Algebra Representation Theory 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. |
| title | Quantum permutation groups |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2012.10975 |