Invariants of a reduced decomposition

Let G be a semi-simple group, provided with an involutorial automorphism whose fixed-point group is K. A Borel group B of G has finitely many orbits in the variety G/K. This paper discusses some invariants attached to a B-orbit: a numerical invariant introduced by R.W. Richardson, and two subsets of the Weyl group. These sets are described in terms of root system data.