{
  "id": "1210.5003",
  "version": "v2",
  "published": "2012-10-18T01:16:28.000Z",
  "updated": "2013-04-22T23:16:16.000Z",
  "title": "Eigenvalues of Hermitian matrices and equivariant cohomology of Grassmannians",
  "authors": [
    "David Anderson",
    "Edward Richmond",
    "Alexander Yong"
  ],
  "comment": "14 pages, to appear in Compositio Math",
  "journal": "Compositio Math. vol 149 (2013), pp 1569-1582",
  "categories": [
    "math.CO"
  ],
  "abstract": "The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of [Klyachko '98], it implies [Horn '62]'s conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization [Friedland '00] to majorized sums of Hermitian matrices. 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 aformentioned work together with [Thomas-Yong '12].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-22T23:16:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hermitian matrices",
      "equivariant cohomology",
      "grassmannians",
      "saturation theorem",
      "eigenvalue problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5003A"
    }
  }
}