Eigenvalues of majorized Hermitian matrices and Littlewood-Richardson coefficients

DOI10.1016/S0024-3795(00)00218-4zbMath0968.15010arXivmath/0209240OpenAlexW1967293344MaRDI QIDQ5926390

William Fulton

Publication date: 12 September 2001

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209240

zbMATH Keywords

Hermitian matricescompact selfadjoint operatorseigenvaluesHilbert spaceinequalities involving eigenvaluesLittlewood-Richardson coefficientSchubert calculustrace equality

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Hermitian, skew-Hermitian, and related matrices (15B57) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06)

Related Items

The limit of the product of the parameterized exponentials of two operators, Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor, Off-diagonal submatrices of a Hermitian matrix, Extremal rays of the equivariant Littlewood-Richardson cone, Eigenvalues of Hermitian matrices with positive sum of bounded rank, Decomposition of a Hermitian matrix into a sum of fixed number of orthogonal projections, Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians, Eigencone, saturation and Horn problems for symplectic and odd orthogonal groups, Klyachko's theorem in semi-finite von Neumann algebras, Quivers, long exact sequences and Horn type inequalities., Non-commutative Schur–Horn theorems and extended majorization for Hermitian matrices, The recursive nature of cominuscule Schubert calculus, Finite and infinite dimensional generalizations of Klyachko's theorem, Quantum generalization of the Horn conjecture, Geometric proofs of Horn and saturation conjectures, A partial Horn recursion in the cohomology of flag varieties, QUIVERS, LONG EXACT SEQUENCES AND HORN TYPE INEQUALITIES II, Principal Submatrices of a Hermitian Matrix, A Geometric Description of Feasible Singular Values in the Tensor Train Format, The sum of unitary similarity orbits containing only special operators, The Horn cone associated with symplectic eigenvalues

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalues of sums of Hermitian matrices
• Stable bundles, representation theory and Hermitian operators
• The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
• Eigenvalues, invariant factors, highest weights, and Schubert calculus
• Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients
• The Multiplication of Schur-Functions and Extensions of p -Modules
• Finite and infinite dimensional generalizations of Klyachko's theorem