تقرير
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
| العنوان: | 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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| المؤلفون: | Douvropoulos, Theo, Lewis, Joel Brewster |
| المصدر: | Hurwitz Orbits on Reflection Factorizations of Parabolic Quasi-Coxeter Elements. Electron. J. Combin. 31 (2024), no. 1, Paper 27 |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Group Theory, 05E18, 20F55, 20F36 |
| الوصف: | 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. Comment: 10 pages, 1 figure, comments very much welcome! v2: minor corrections; simplification of one argument in Section 2 (and consequent renumbering) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.37236/11787 |
| URL الوصول: | http://arxiv.org/abs/2209.00774 |
| رقم الأكسشن: | edsarx.2209.00774 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.37236/11787 |
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