Dominant weight associated with actions of real reductive groups (Q6141356)

The paper is inspired by results concerning the dominant weight associated with the Hamiltonian action of a complex reductive group on a Kähler manifold. The author extends these results to the action of a real reductive Lie group on a real submanifold of a Kähler manifold. Stability theory in Kähler geometry has been studied in great detail using different techniques. One main ingredient for the proof of the Hilbert-Mumford criterion, which relates stability conditions with the numerical value \(\lambda(x,\beta)\), is the moment weight inequality. The author further investigates this inequality by studying the dominant weight's existence and uniqueness under various stability conditions.