A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements
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- by Barbara Baumeister, Matthew Dyer, Christian Stump and Patrick Wegener HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 149-154
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.References
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Additional Information
- Barbara Baumeister
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
- MR Author ID: 350609
- Email: b.baumeister@math.uni-bielefeld.de
- Matthew Dyer
- Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556
- MR Author ID: 292327
- Email: matthew.j.dyer.1@nd.edu
- Christian Stump
- Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
- MR Author ID: 904921
- ORCID: 0000-0002-9271-8436
- Email: christian.stump@fu-berlin.de
- Patrick Wegener
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
- MR Author ID: 1091992
- Email: patrick.wegener@math.uni-bielefeld.de
- 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
- © Copyright 2014 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- 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
- MathSciNet review: 3294251