2 citations · 3 across the 11 of their papers we have counts for
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Hurwitz Equivalence of Reflection Factorizations in Types and
Patrick Wegener
A conjecture of Lewis asserts that two reflection factorizations of the same element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the…
Commutators of signed -cycles
Philipp Bader, Bernhard Böhmler, Patrick Wegener
We show that for each element of the commutator subgroup in the symmetric group resp. in the signed symmetric group $(\mathbb{Z}/2\mathbb{Z})^n\rtimes\m…
The Hurwitz Action in the Affine Symmetric Group
Patrick Wegener
Let be an affine Coxeter group of type , that is, the affine symmetric group with , let be its set of reflections, and let $\mathr…
The hyperbolic cover of an elliptic Weyl group
Barbara Baumeister, Patrick Wegener
In this paper, we study in detail the hyperbolic covers and of an elliptic Weyl system introduced by Saito. We show that they are isomorphic and also isomorph…
Reflection factorizations and quasi-Coxeter elements
Patrick Wegener, Sophiane Yahiatene
We investigate the so-called dual Matsumoto property or Hurwitz action in finite, affine and arbitrary Coxeter groups. In particular, we want to investigate how to reduce reflectio…
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.
On the Hurwitz action in affine Coxeter groups
Patrick Wegener
We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced factorizations into a product of reflections is transitive. W…
A note on Weyl groups and crystallographic root lattices
Barbara Baumeister, Patrick Wegener
We follow the dual approach to Coxeter systems and show for Weyl groups a criterium which decides whether a set of reflections is generating the group depending on the root and the…
On the Hurwitz action in finite Coxeter groups
Barbara Baumeister, Thomas Gobet, Kieran Roberts +1
We provide a necessary and sufficient condition on an element of a finite Coxeter group to ensure the transitivity of the Hurwitz action on its set of reduced decompositions into p…
A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements
Barbara Baumeister, Matthew Dyer, Christian Stump +1
In this note, we provide a short and self-contained proof that the braid group on n strands acts transitively on the set of reduced factorizations of a Coxeter element in a Coxeter…