Geodesic
Hurwitz orbits on reflection factorizations of parabolic quasi-Coxeter elements
Theo Douvropoulos1 ; Joel Brewster Lewis2
1UMass
2George Washington University
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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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.
DOI : 10.37236/11787
Classification : 20F36, 20F55, 05E18
Mots-clés : Coxeter group, parabolic quasi-Coxeter element, Hurwitz orbit, conjugacy class, generating set

Theo Douvropoulos  1   ; Joel Brewster Lewis  2

1 UMass
2 George Washington University 
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     author = {Theo Douvropoulos and Joel Brewster Lewis},
     title = {Hurwitz orbits on reflection factorizations of parabolic {quasi-Coxeter} elements},
     journal = {The electronic journal of combinatorics},
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Theo Douvropoulos; Joel Brewster Lewis. Hurwitz orbits on reflection factorizations of parabolic quasi-Coxeter elements. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11787

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