Asymptotical behaviour of roots of infinite Coxeter groups I
Abstrak
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 $E$.
Topik & Kata Kunci
Penulis (3)
Christophe Hohlweg
Jean-Philippe Labbé
Vivien Ripoll
Akses Cepat
- Tahun Terbit
- 2012
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.3088
- Akses
- Open Access ✓