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Proceedings of the American Mathematical Society Series B

ISSN 2330-1511

   
 
 

 

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


Authors: Barbara Baumeister, Matthew Dyer, Christian Stump and Patrick Wegener
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 149-154
MSC (2010): Primary 20F55
DOI: https://doi.org/10.1090/S2330-1511-2014-00017-1
Published electronically: December 31, 2014
MathSciNet review: 3294251
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Abstract: 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$ also lie in this parabolic subgroup.


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Additional Information

Barbara Baumeister
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Email: b.baumeister@math.uni-bielefeld.de

Matthew Dyer
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556
Email: matthew.j.dyer.1@nd.edu

Christian Stump
Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
Email: christian.stump@fu-berlin.de

Patrick Wegener
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Email: patrick.wegener@math.uni-bielefeld.de

DOI: https://doi.org/10.1090/S2330-1511-2014-00017-1
Received by editor(s): February 12, 2014
Received by editor(s) in revised form: July 9, 2014
Published electronically: December 31, 2014
Additional Notes: The first and fourth authors were supported by the DFG through SFB 701 “Spectral Structures and Topological Methods in Mathematics”.
The third author was supported by the DFG through STU 563/2-1 “Coxeter-Catalan combinatorics”.
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)