{
  "id": "2102.00870",
  "version": "v1",
  "published": "2021-02-01T14:27:12.000Z",
  "updated": "2021-02-01T14:27:12.000Z",
  "title": "Representations of involutory subalgebras of affine Kac-Moody algebras",
  "authors": [
    "Axel Kleinschmidt",
    "Ralf Köhl",
    "Robin Lautenbacher",
    "Hermann Nicolai"
  ],
  "comment": "37 pages",
  "categories": [
    "math.RT",
    "hep-th"
  ],
  "abstract": "We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful representations. We exhibit a formulation of these algebras in terms of $\\mathbb{N}$-graded Lie algebras that allows the construction of a large class of representations using the techniques of induced representations. We study how these representations relate to previously established spinor representations as they arise in the theory of supergravity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T14:27:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine kac-moody algebras",
      "involutory subalgebras",
      "non-twisted affine kac-moody lie algebras",
      "infinite-dimensional lie algebras",
      "admit finite-dimensional unfaithful representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}