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Conjugacy of Coxeter elements
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2009 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed) Published
Abstract [en]

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
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-24368ISI: 000263969200001OAI: oai:DiVA.org:kth-24368DiVA: diva2:349148
Note
QC 20100906Available from: 2010-09-06 Created: 2010-09-06 Last updated: 2017-12-12Bibliographically approved

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