Details
| Original language | English |
|---|---|
| Article number | 106308 |
| Journal | Journal of Pure and Applied Algebra |
| Volume | 224 |
| Issue number | 7 |
| Early online date | 7 Jan 2020 |
| Publication status | Published - Jul 2020 |
| Externally published | Yes |
Abstract
We call an element of a Coxeter group a parabolic quasi-Coxeter element if it has a reduced decomposition into a product of reflections that generate a parabolic subgroup. We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced decompositions into a product of reflections is transitive.
Keywords
- Coxeter groups, Hurwitz action, Reflection decompositions
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Pure and Applied Algebra, Vol. 224, No. 7, 106308, 07.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Hurwitz action in affine Coxeter groups
AU - Wegener, Patrick
PY - 2020/7
Y1 - 2020/7
N2 - We call an element of a Coxeter group a parabolic quasi-Coxeter element if it has a reduced decomposition into a product of reflections that generate a parabolic subgroup. We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced decompositions into a product of reflections is transitive.
AB - We call an element of a Coxeter group a parabolic quasi-Coxeter element if it has a reduced decomposition into a product of reflections that generate a parabolic subgroup. We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced decompositions into a product of reflections is transitive.
KW - Coxeter groups
KW - Hurwitz action
KW - Reflection decompositions
UR - http://www.scopus.com/inward/record.url?scp=85077722093&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2020.106308
DO - 10.1016/j.jpaa.2020.106308
M3 - Article
VL - 224
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 7
M1 - 106308
ER -