Conjugacy of Coxeter elements
2009 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed) Published
For a Coxeter group (W, S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Coxeter elements are conjugate if and only if they are rotation equivalent. This was known for some special cases but not for Coxeter groups in general.
Place, publisher, year, edition, pages
2009. Vol. 16, no 2
IdentifiersURN: urn:nbn:se:kth:diva-24368ISI: 000263969200001OAI: oai:DiVA.org:kth-24368DiVA: diva2:349148
QC 201009062010-09-062010-09-062010-09-21Bibliographically approved