A symplectic proof of the Horn inequalities
Symplectic Geometry
2014-10-14 v1 Representation Theory
Abstract
In this paper, we give a symplectic proof of the Horn inequalities on eigenvalues of a sum of two Hermitian matrices with given spectra. Our method is a combination of tropical calculus for matrix eigenvalues, combinatorics of planar networks, and estimates for the Liouville volume. As a corollary, we give a tropical description of the Duistermaat-Heckman measure on the Horn polytope.
Keywords
Cite
@article{arxiv.1410.3149,
title = {A symplectic proof of the Horn inequalities},
author = {Anton Alekseev and Masha Podkopaeva and Andras Szenes},
journal= {arXiv preprint arXiv:1410.3149},
year = {2014}
}