English

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}
}

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12 pages