Geometrical classification scheme for weights of Lie algebras

Every weight of a Lie algebra belongs to one particular Weyl orbit. The depth within an orbit has been defined as the minimum number of Weyl reflections associated with simple roots that are necessary to transform the weight into the dominant weight of the orbit. A simple set of classification parameters that measures the depth and distinguishes between different weights of the same depth is introduced. The parameters are geometrical in that they are related directly to the orientation of the weight vector. They correspond to a particular member of the Weyl group that transforms the weight into the dominant weight. A simple rule is given for listing all the weights of an orbit in terms of the parameters