Eigenvalues of majorized Hermitian matrices and Littlewood–Richardson coefficients

By William Fulton. 2000

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7316c992187afe428dc7242216887294f663a705

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Eigenvalues, singular values, and Littlewood-Richardson coefficients (2003, methodology): “Examples. We next summarize the main result of [13], which includes the main result of [ 8 ], in a form suitable for our purposes.”
Geometric proofs of horn and saturation conjectures (2002, background): “The above proposition also relates closely to ideas in Fulton [ 7 ], Proposition 1: Use notation from the preceding discussion.”