Abstract :
This paper contains several results concerning convex orderings in root systems. These results complete the analysis developed in earlier papers by the author. We obtain, in the finite case, a combinatorial characterization of reflections, longest elements in standard parabolic subgroups of the Weyl group of the root system, and of Coxeter elements. In the affine case, a refinement of the main construction done earlier by the author (J. Algebra172, 1995, 613–623) is described; moreover, infinite periodic compatible sets are classified.
