{
  "id": "2406.19862",
  "version": "v1",
  "published": "2024-06-28T12:07:00.000Z",
  "updated": "2024-06-28T12:07:00.000Z",
  "title": "Reflection operator and hypergeometry I: $SL(2, \\mathbb{R})$ spin chain",
  "authors": [
    "P. Antonenko",
    "N. Belousov",
    "S. Derkachov",
    "S. Khoroshkin"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT",
    "nlin.SI"
  ],
  "abstract": "In this work we consider open $SL(2, \\mathbb{R})$ spin chain, mainly the simplest case of one particle. Eigenfunctions of the model can be constructed using the so-called reflection operator. We obtain several representations of this operator and show its relation to the hypergeometric function. Besides, we prove orthogonality and completeness of one-particle eigenfunctions and connect them to the index hypergeometric transform. Finally, we briefly state the formula for the eigenfunctions in many-particle case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-28T12:07:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin chain",
      "reflection operator",
      "hypergeometry",
      "index hypergeometric transform",
      "simplest case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}