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- W2963804823 abstract "Let $W$ be an infinite Coxeter group, and $Phi$ be the root system constructed from its geometric representation. We study the set $E$ of limit points of normalized'' roots (representing the directions of the roots). We show that $E$ is contained in the isotropic cone $Q$ of the bilinear form associated to $W$, and illustrate this property with numerous examples and pictures in rank $3$ and $4$. We also define a natural geometric action of $W$ on $E$, for which $E$ is stable. Then we exhibit a countable subset $E_2$ of $E$, formed by limit points for the dihedral reflection subgroups of $W$; we explain how $E_2$ can be built from the intersection with $Q$ of the lines passing through two roots, and we establish that $E_2$ is dense in $E$. Soit $W$ un groupe de Coxeter infini, et $Phi$ le système de racines construit à partir de sa représentation géométrique. Nous étudions l'ensemble $E$ des points d'accumulation des racines normalisées'' (représentant les directions des racines). Nous montrons que $E$ est inclus dans le cône isotrope $Q$ de la forme bilinéaire associée à $W$, et nous illustrons cette propriété à l'aide de nombreux exemples et images en rang $3$ et $4$. Nous définissons une action géométrique naturelle de $W$ sur $E$, pour laquelle $E$ est stable. Puis nous présentons un sous-ensemble dénombrable $E_2$ de $E$, constitué des points d'accumulation associés aux sous-groupes de réflexion diédraux de $W$ ; nous expliquons comment $E$ peut être construit à partir des points d'intersection de $Q$ avec les droites passant par deux racines, et nous montrons que $E_2$ est dense dans $E$." @default.
- W2963804823 created "2019-07-30" @default.
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- W2963804823 date "2012-01-01" @default.
- W2963804823 modified "2023-10-04" @default.
- W2963804823 title "Asymptotical behaviour of roots of infinite Coxeter groups I" @default.
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- W2963804823 doi "https://doi.org/10.46298/dmtcs.3088" @default.
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