Differential contra algebraic invariants: Applications to classical algebraic problems

Abstract

In this paper we discuss an approach to the study of orbits of actions of semisimple Lie groups in their irreducible complex representations,which is based on differential invariants on the one hand, and on geometry of reductive homogeneous spaces on the other hand. According to the Borel–Weil–Bott theorem, every irreducible representation of semisimple Lie group is isomorphic to the action of this group on the module of holomorphic sections of some one–dimensional bundle over homogeneous space. Using this, we give a complete description of the structure of the field of differential invariants for this action and obtain a criterion which separates regular orbits.