Honeycombs and sums of Hermitian matrices

Details Honeycombs and sums of Hermitian matrices Honeycombs and sums of Hermitian matrices

2000-09-06

arxiv.org/abs/math/0009048v1

Mathematics

Representation Theory

16 pages, 14 figures, submitted, Notices Amer. Math. Soc

Scientific paper

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.

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