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Hurwitz Equivalence of Reflection Factorizations in Types B and D

  • Patrick Wegener
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Abstract

A conjecture of Lewis asserts that two reflection factorizations of the same element in a finite Coxeter group W belong to the same Hurwitz orbit if and only if they generate the same subgroup H of W and have the same multiset of H-conjugacy classes. We prove this conjecture for every finite Coxeter group all of whose irreducible components are of type A, B or D. Furthermore we prove a reduction, which reduces the conjecture to a finite problem for the exceptional types.

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Cite

BibTeXRIS
BibTeX
@misc{wegener2026hurwitz,
  title = {{Hurwitz Equivalence of Reflection Factorizations in Types $B$ and $D$}},
  author = {Patrick Wegener},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27060},
  eprint = {2609.27060},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27060},
}
RIS
TY  - UNPB
TI  - Hurwitz Equivalence of Reflection Factorizations in Types B and D
AU  - Patrick Wegener
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27060
UR  - https://arxiv.org/abs/2609.27060
AB  - A conjecture of Lewis asserts that two reflection factorizations of the same element in a finite Coxeter group W belong to the same Hurwitz orbit if and only if they generate the same subgroup H of W and have the same multiset of H-conjugacy classes. We prove this conjecture for every finite Coxeter group all of whose irreducible components are of type A, B or D. Furthermore we prove a reduction, which reduces the conjecture to a finite problem for the exceptional types.
ER  -