A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements-Reference-Cited by-同舟云学术

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

Published:2014-12-31 Issue:13 Volume:1 Page:149-154
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Baumeister Barbara,Dyer Matthew,Stump Christian,Wegener Patrick

Abstract

In this note, we provide a short and self-contained proof that the braid group on n n strands acts transitively on the set of reduced factorizations of a Coxeter element in a Coxeter group of finite rank n 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 W also lie in this parabolic subgroup.

Publisher

American Mathematical Society (AMS)

Subject

General Medicine

Link

http://www.ams.org/bproc/2014-01-13/S2330-1511-2014-00017-1/S2330-1511-2014-00017-1.pdf

Reference10 articles.

1. The dual braid monoid;Bessis, David;Ann. Sci. \'{E}cole Norm. Sup. (4),2003

2. [Del74] P. Deligne, letter to E. Looijenga, 9/3/1974. available at \url{http://homepage.univie.ac.at/christian.stump/ Deligne_{L}ooijenga_{L}etter_{0}9-03-1974.pdf.}

3. Présentations duales des groupes de tresses de type affine ̃𝐴;Digne, F.;Comment. Math. Helv.,2006

4. On minimal lengths of expressions of Coxeter group elements as products of reflections;Dyer, Matthew J.;Proc. Amer. Math. Soc.,2001

5. Reflection subgroups of Coxeter systems;Dyer, Matthew;J. Algebra,1990

Cited by 19 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements;Journal of Algebra;2024-03

2. Interval groups related to finite Coxeter groups Part II;Transactions of the London Mathematical Society;2023-09-27

3. Interval groups related to finite Coxeter groups I;Algebraic Combinatorics;2023-05-03

4. Geometric description of C-vectors and real Lösungen;Mathematische Zeitschrift;2023-01-12

5. Virtual Artin groups;Proceedings of the London Mathematical Society;2022-10-31