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.
Keywords Inequality - majorization - symmetric function
Mathematics Subject Classification (2000) 52A40 - 26D05 - 60E15
Supported in part by the National Science Foundation and the Center for the Mathematics of Information.