We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...