{
  "id": "2405.20177",
  "version": "v1",
  "published": "2024-05-30T15:45:40.000Z",
  "updated": "2024-05-30T15:45:40.000Z",
  "title": "On the nested algebraic Bethe ansatz for spin chains with simple $\\mathfrak{g}$-symmetry",
  "authors": [
    "Allan John Gerrard"
  ],
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "math.QA",
    "nlin.SI"
  ],
  "abstract": "We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\\mathfrak{g}$-symmetry for any simple Lie algebra $\\mathfrak{g}$. Starting the nesting process by removing a single simple root from $\\mathfrak{g}$, we use the residual $U(1)$ charge and the block Gauss decomposition of the $R$-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-30T15:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nested algebraic bethe ansatz",
      "simple lie algebra",
      "rational spin chain",
      "single simple root",
      "block gauss decomposition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}