3 papers
math.GR2019
The centralizer of a Coxeter element
Ruwen Hollenbach, Patrick Wegener
We prove that the centralizer of a Coxeter element in an irreducible Coxeter group is the cyclic group generated by that Coxeter element.
math.CO2019
Reflection groups and quiver mutation: Diagrammatics
Patrick Wegener
We extend Carter's notion of admissible diagrams and attach a "Dynkin-like" diagram to each reduced reflection factorization of an element in a finite Weyl group. We give a complet…
math.CO2019
A note on non-reduced reflection factorizations of Coxeter elements
Patrick Wegener, Sophiane Yahiatene
We extend a result of Lewis and Reiner from finite Coxeter groups to all Coxeter groups by showing that two reflection factorizations of a Coxeter element lie in the same Hurwitz o…