Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients
Rings and Algebras
2007-05-23 v1 Commutative Algebra
Algebraic Geometry
Abstract
Answering a question raised by S. Friedland, we show that the possible eigenvalues of Hermitian matrices (or compact operators) A, B, and C with C <= A + B are given by the same inequalities as in Klyachko's theorem for the case where C = A + B, except that the equality corresponding to tr(C) = tr(A) + tr(B) is replaced by the inequality corresponding to tr(C) <= tr(A) + tr(B). The possible types of finitely generated torsion modules A, B, and C over a discrete valuation ring such that there is an exact sequence B -> C -> A are characterized by the same inequalities.
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Cite
@article{arxiv.math/0209240,
title = {Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients},
author = {William Fulton},
journal= {arXiv preprint arXiv:math/0209240},
year = {2007}
}
Comments
12 pages