Timeline for Reference request: which elements in a Coxeter group has longest reflection length?
Current License: CC BY-SA 4.0
4 events
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| Dec 19, 2018 at 18:38 | comment | added | Sam Hopkins | Sorry, what I said above was wrong: the Coxeter elements are not all the maximal elements wrt absolute order. Quoting from pg. 30 of Armstrong "In the case of the symmetric group, the Coxeter elements are precisely the maximal elements of the absolute order; in all other cases, the Coxeter elements are a proper subclass of maximal elements." | |
| Dec 19, 2018 at 17:27 | comment | added | Sam Hopkins | Armstrong's oft-cited monograph has a good introduction to absolute order and Coxeter elements: arxiv.org/abs/math/0611106 | |
| Dec 19, 2018 at 17:19 | comment | added | Sam Hopkins | You should look up "absolute order." The maximal elements in absolute order are the Coxeter elements (=products of all the simple reflections in some order, and their conjugates). | |
| Dec 19, 2018 at 17:13 | history | asked | Jianrong Li | CC BY-SA 4.0 |