Muirhead-Rado inequality for compact groups

Muirhead’s majorization inequality was extended by Rado to the case of arbitrary permutation groups. We further generalize this inequality to compact groups and their linear representations over the reals. We characterize saturation of the inequality, and describe the saturation condition in detail for the case of actions on Hermitian operators. Supported in part by the National Science Foundation and the Center for the Mathematics of Information.