{
  "id": "2203.12992",
  "version": "v1",
  "published": "2022-03-24T11:32:53.000Z",
  "updated": "2022-03-24T11:32:53.000Z",
  "title": "LS Algebras, Valuations and Schubert Varieties",
  "authors": [
    "Rocco Chirivì",
    "Xin Fang",
    "Peter Littelmann"
  ],
  "categories": [
    "math.AG",
    "math.AC",
    "math.CO",
    "math.RT"
  ],
  "abstract": "In this paper, we propose an algebraic approach via Lakshmibai-Seshadri (LS) algebras to establish a link between standard monomial theories, Newton-Okounkov bodies and valuations. This is applied to Schubert varieties, where this approach is compatible with the one using Seshadri stratifications by the same authors (arXiv:2112.03776), showing that LS paths encode vanishing multiplicities with respect to the web of Schubert varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-24T11:32:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "14M25"
    ],
    "keywords": [
      "schubert varieties",
      "ls algebras",
      "valuations",
      "ls paths encode vanishing multiplicities",
      "standard monomial theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}