Quotients compacts des groupes ultrametriques de rang un

Représentations de réflexion de groupes de Coxeter Sixième partie: le cas réductible; exemples en rang trois

In this sixth part we study rank $3$ reflection groups not well generated: $G(2r,r,2)$, $G_{12}$, $G_{13}$ and $G_{22}$. We start from a reflection representation of a rank $3$ Coxeter group and we show that we can obtain in this manner affine Coxeter groups whose linear part is one of the preceding groups.

Représentations de réflexion de groupes de Coxeter Cinquième partie: La représentation $R$ est réductible. Cas particulier du rang $3$

In this fith part, (with the notations of the preceding parts) we make the following hypothesis: $(W,S)$ is a Coxeter system, irreducible, $2$-spherical and $S$ is of cardinality $3$. Let $R:W\to GL(M)$ be a reducible reflection representation of $W$. Let $G:= Im\,R$. Each sub-space of $M$ $(\neq M)$ stabilize by $G$ is contained in $C_{M}(G)$. Let $M':=M/C_{M}(G)$ and $N(G):=\{g|g\in G,g\, \text{acts trivially on}\,M'\}$. We call $N(G)$ the translation sub-group of $G$. One of the goals of this part is to study $M'$ and $N(G)$. In particular it is shown that $N(G)$ is an $\mathcal{O}G-module$…

Groupes convexes-cocompacts en rang supérieur

The convex-cocompact subgroups are central in hyperbolic geometry and more generally in negative curvature. Labourie introduced in 2005 the notion of 'Anosov' subgroup which proves progressively to be the right generalizations of convex-cocompact groups, especially after the works of Kapovich, Leeb and Porti. This exposé will review different caracteriations of those groups, emphasizing the parallel (or difference) with the negative curvature, and will give their basic properties.

经由 E_6 型 Weyl 群构造 Shephard-Todd 群 G_{32}

Une construction du groupe $G_{32}$ de Shephard-Todd via le groupe de Weyl de type $E_6$

本文证明 Shephard-Todd 复反射群 G_{32} 的导群模中心与 E_6 型 Weyl 群导群的同构可由第二外幂实现，并据此给出 G_{32} 的替代构造。