 However, there is a general explanation why most of the pairs ("G","V") in the classification are prehomogeneous, in terms of isotropy representations of generalized flag varieties.Indeed, in 1974, Richardson observed that if "H" is a semisimple Lie group with a parabolic subgroup "P", then the action of "P" on the nilradical formula_9 of its Lie algebra has a dense open orbit.This shows in particular (and was noted independently by Vinberg in 1975) that the Levi factor "G" of "P" acts prehomogeneously on formula_10.