Convex Orderings in Affine Root Systems, II Original Research Article

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.