Parabolic subgroups of positive modality
The author proves a criterion for a parabolic subgroup \(P\) of a reductive algebraic group \(G\) to be of positive modality. This condition is simply a lower bound on the length of the descending central series of the radical. He also shows that in this situation we can always find a proper \(P\)-invariant linear subspace in the Lie algebra of the radical of \(P\) which admits an infinite number of \(P\)-orbits, unless \(P\) is maximal.
scientific article; zbMATH DE number 874091