Asymptotical behaviour of roots of infinite Coxeter groups

Hohlweg, Christophe; Labbé, Jean-Philippe et Ripoll, Vivien (2014). « Asymptotical behaviour of roots of infinite Coxeter groups ». Canadian Journal of Mathematics, 66(2), pp. 323-353.

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Let W be an infinite Coxeter group. We initiate the study of the set E of limit points of ``normalized'' roots (representing the directions of the roots) of W. We show that E is contained in the isotropic cone Q of the bilinear form B associated to a geometric representation, and illustrate this property with numerous examples and pictures in rank 3 and 4. We also define a natural geometric action of W on E, and then we exhibit a countable subset of E, formed by limit points for the dihedral reflection subgroups of W. We explain how this subset is built from the intersection with Q of the lines passing through two positive roots, and finally we establish that it is dense in E.

Type: Article de revue scientifique
Mots-clés ou Sujets: Coxeter group, root system, roots, limit point, accumulation set.
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Christophe Hohlweg
Date de dépôt: 15 févr. 2016 15:05
Dernière modification: 20 avr. 2016 19:30
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