Honeycombs and sums of Hermitian matrices
Representation Theory
2009-09-25 v1 Rings and Algebras
Abstract
Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce a combinatorial gadget called a {\em honeycomb}; the question is then reformulable as about the existence of honeycombs with certain boundary conditions. Another important tool is the connection to the representation theory of the group U(n), by ``classical vs. quantum'' analogies.
Cite
@article{arxiv.math/0009048,
title = {Honeycombs and sums of Hermitian matrices},
author = {Allen Knutson and Terence Tao},
journal= {arXiv preprint arXiv:math/0009048},
year = {2009}
}
Comments
16 pages, 14 figures, submitted, Notices Amer. Math. Soc