{
  "id": "2307.13671",
  "version": "v1",
  "published": "2023-07-25T17:31:47.000Z",
  "updated": "2023-07-25T17:31:47.000Z",
  "title": "The cohomology of the Quot scheme on a smooth curve as a Yangian representation",
  "authors": [
    "Alina Marian",
    "Andrei Neguţ"
  ],
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We describe the action of the shifted Yangian of sl_2 on the cohomology groups of the Quot schemes of 0-dimensional quotients on a smooth projective curve. We introduce a commuting family of r operators in the positive half of the Yangian, whose action yields a natural basis of the Quot cohomology. These commuting operators further lead to formulas for the operators of multiplication by the Segre classes of the universal bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-25T17:31:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quot scheme",
      "smooth curve",
      "yangian representation",
      "natural basis",
      "smooth projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}