Eigenvalues of hermitian matrices and equivariant cohomology of grassmannians

David Anderson, Edward Richmond, Alexander Yong

Research output: Contribution to journalArticlepeer-review


The saturation theorem of Knutson and Tao concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of Klyachko, it implies Horn's conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization to majorized sums of Hermitian matrices, due to S. Friedland. We further illustrate the common features between these two eigenvalue problems and their connection to Schubert calculus of Grassmannians. Our main result gives a Schubert calculus interpretation of Friedland's problem, via equivariant cohomology of Grassmannians. In particular, we prove a saturation theorem for this setting. Our arguments employ the aforementioned work together with recent work of H. Thomas and A. Yong.

Original languageEnglish (US)
Pages (from-to)1569-1582
Number of pages14
JournalCompositio Mathematica
Issue number9
StatePublished - Sep 2013


  • Schubert calculus
  • eigenvalue problem
  • equivariant cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory


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