Hurwitz Orbits on Reflection Factorizations of Parabolic Quasi-Coxeter Elements

  • Theo Douvropoulos
  • Joel Brewster Lewis


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.

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