A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements

By B. Baumeister, M. Dyer, Christian Stump, Patrick Wegener. 2014

58 citations recorded by the source corpus.

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 group of finite rank n into products of reflections. We moreover use the same argument to also show that all factorizations of an element in a parabolic subgroup of W lie as well in this parabolic subgroup.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/af9bed156af3205879314e28d7eedd53dd8030bb

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

A categorification of non-crossing partitions (2013, methodology): “As an application to Coxeter systems, we note that in [2] it is shown that the factorisations of a parabolic Coxeter element form a single orbit under the braid group action.”
Artin groups of Euclidean type (2013, background): “action on reﬂection factorizations of Coxeter elements in Coxeter groups in complete generality [IS10] and in 2014 a short proof of this general fact was posted by Baumeister, Dyer, Stump and Wegener [BDSW14]. As an illustration, we give the Hurwitz presentation of the dual G 2 Artin group. We start”