{
  "id": "2104.09929",
  "version": "v1",
  "published": "2021-04-20T12:34:45.000Z",
  "updated": "2021-04-20T12:34:45.000Z",
  "title": "Newton-Okounkov polytopes of flag varieties and marked chain-order polytopes",
  "authors": [
    "Naoki Fujita"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG",
    "math.CO",
    "math.RT"
  ],
  "abstract": "Marked chain-order polytopes are convex polytopes constructed from a marked poset, which give a discrete family relating a marked order polytope with a marked chain polytope. In this paper, we consider the Gelfand-Tsetlin poset of type A, and realize the associated marked chain-order polytopes as Newton-Okounkov bodies of the flag variety. Our realization connects previous realizations of Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg polytopes as Newton-Okounkov bodies in a uniform way. As an application, we prove that the flag variety degenerates into the irreducible normal projective toric variety corresponding to a marked chain-order polytope. We also construct a specific basis of an irreducible highest weight representation which is naturally parametrized by the set of lattice points in a marked chain-order polytope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-20T12:34:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "05E10",
      "06A07",
      "14M15",
      "52B20"
    ],
    "keywords": [
      "marked chain-order polytope",
      "newton-okounkov polytopes",
      "newton-okounkov bodies",
      "irreducible highest weight representation",
      "irreducible normal projective toric variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}