In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916116608057344 |
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| author | Douvropoulos, Theo Lewis, Joel Brewster |
| author_facet | Douvropoulos, Theo Lewis, Joel Brewster |
| contents | We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same subgroup and have the same multiset of conjugacy classes. As a lemma, we classify the finite Coxeter groups for which every reflection generating set that is minimal under inclusion is also of minimum size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00774 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants Douvropoulos, Theo Lewis, Joel Brewster Combinatorics Group Theory 05E18, 20F55, 20F36 We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same subgroup and have the same multiset of conjugacy classes. As a lemma, we classify the finite Coxeter groups for which every reflection generating set that is minimal under inclusion is also of minimum size. |
| title | In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants |
| topic | Combinatorics Group Theory 05E18, 20F55, 20F36 |
| url | https://arxiv.org/abs/2209.00774 |