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# Title: Honeycombs and sums of Hermitian matrices

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.
 Comments: 16 pages, 14 figures, submitted, Notices Amer. Math. Soc Subjects: Representation Theory (math.RT); Rings and Algebras (math.RA) MSC classes: 15A42, 17B10; 22E47, 52B20, 53B20 Cite as: arXiv:math/0009048 [math.RT] (or arXiv:math/0009048v1 [math.RT] for this version)

## Submission history

From: Terence C. Tao [view email]
[v1] Wed, 6 Sep 2000 04:07:17 GMT (41kb)
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