Invariants of algebraic group actions from differential point of view (Q669582)

This paper proposes an approach to study invariants of algebraic representations for connected semi-simple complex algebraic groups \(G\) based on the famous Borel-Weil-Bott theorem. A Borel subgroup \(B\) defines the homogeneous complex flag manifold \(M:=G/B\) and the bundle \(\pi ^{\lambda}: G\times _B\mathbb{C}^n\rightarrow M\). The authors consider the jet space of the sections of the bundle \(\pi ^{\lambda }\) and describe the differential invariant field of the \(G\)-action on the jets of sections.