Eigenvalues, singular values, and Littlewood-Richardson coefficients
By Sergey Fomin, William Fulton, Chi-Kwong Li, Yiu-Tung Poon. 2003
78 citations recorded by the source corpus.
We characterize the relationship between the singular values of a Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of a Hermitian (or real symmetric) matrix C = A + B in terms of the combined list of eigenvalues of A and B . The answers are given by Horn-type linear inequalities. The proofs depend on a new inequality among Littlewood-Richardson coefficients.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/dc0ece12d78aa2b43f599d18b650273023143471
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In Algebra and Number Theory
- Hugh Thomas
- Alexander Yong
- Larry X. W. Wang
- Alexander A. Klyachko
- William Y. C. Chen
- I. Reiten
- Lingyan Guo
- B. Keller
In Discrete Mathematics and Combinatorics
- Hugh Thomas
- Alexander Yong
- Arthur L. B. Yang
- Larry X. W. Wang
- Alexander A. Klyachko
- William Y. C. Chen
- I. Reiten
- Lingyan Guo
In Statistical and Nonlinear Physics
Citations in the corpus
- QUANTUM MARGINAL PROBLEM AND REPRESENTATIONS OF THE SYMMETRIC GROUP (2004, background): “by linear inequalities in SpecH and singular spectrum of X [31, 11].”
- Schur positivity and the q-log-convexity of the Narayana polynomials (2008, background): “Notice that much work has been done on the Schur positivity of differences of products of Schur functions; see, for example, Bergeron, Biagioli and Rosas [2], Fomin, Fulton, Li and Poon [11] and Okounkov [23].”
- A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, methodology): “This conjecture generalizes a theorem in the cohomological case due to [LaPoPy05]; see related work by [Ok03, FoFuLiPo05 , ChDeWe07].”