Subgroup Majorization

Andrew R. Francis; Henry P. Wynn

doi:10.1016/j.laa.2013.11.042

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arXiv · 1303.2707

Subgroup Majorization

Andrew R. Francis·Henry P. Wynn

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Abstract

The extension of majorization (also called the rearrangement ordering), to more general groups than the symmetric (permutation) group, is referred to as $G$-majorization. There are strong results in the case that $G$ is a reflection group and this paper builds on this theory in the direction of subgroups, normal subgroups, quotient groups and extensions. The implications for fundamental cones and order-preserving functions are studied. The main example considered is the hyperoctahedral group, which, acting on a vector in $\mathbb R^n$, permutes and changes the signs of components.

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Andrew R. Francis, Henry P. Wynn. 2013-03-11. Subgroup Majorization. https://doi.org/10.1016/j.laa.2013.11.042

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