{
  "id": "0906.5189",
  "version": "v4",
  "published": "2009-06-29T01:12:14.000Z",
  "updated": "2011-12-23T18:15:53.000Z",
  "title": "Irreducible finite-dimensional representations of equivariant map algebras",
  "authors": [
    "Erhard Neher",
    "Alistair Savage",
    "Prasad Senesi"
  ],
  "comment": "25 pages; v2: results generalized to schemes and arbitrary finite-dimensional g; v3: change of notation, minor typos corrected, some explanations added; v4: minor typos corrected and references updated",
  "journal": "Trans. Amer. Math. Soc., 364 (2012), no. 5, 2619-2646",
  "doi": "10.1090/S0002-9947-2011-05420-6",
  "categories": [
    "math.RT",
    "math.AG",
    "math.RA"
  ],
  "abstract": "Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional representations of these algebras. In particular, we show that all such representations are tensor products of evaluation representations and one-dimensional representations, and we establish conditions ensuring that they are all evaluation representations. For example, this is always the case if M is perfect. Our results can be applied to multiloop algebras, current algebras, the Onsager algebra, and the tetrahedron algebra. Doing so, we easily recover the known classifications of irreducible finite-dimensional representations of these algebras. Moreover, we obtain previously unknown classifications of irreducible finite-dimensional representations of other types of equivariant map algebras, such as the generalized Onsager algebra.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-12-23T18:15:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B20",
      "17B65"
    ],
    "keywords": [
      "irreducible finite-dimensional representations",
      "evaluation representations",
      "corresponding equivariant map algebra",
      "finite-dimensional lie algebra",
      "equivariant regular maps"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.5189N"
    }
  }
}