Ladder operators of the de Sitter algebra

We identify raising and lowering operators of the de Sitter algebra with focus on their action on states in particular in 4 spacetime dimensions. There isn’t a unique solution to the question of how the de Sitter ladder operators act on states. By fixing the action of certain generators one can conclude on the action of the rest. Our main aim is to be able to identify highest and lowest weight states such that we can recognize them for quantized fields on a rigid de Sitter background.