{
  "id": "2203.13033",
  "version": "v1",
  "published": "2022-03-24T12:24:57.000Z",
  "updated": "2022-03-24T12:24:57.000Z",
  "title": "Affine Lie algebras representations induced from Whittaker modules",
  "authors": [
    "Maria Clara Cardoso",
    "Vyacheslav Futorny"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary Affine Kac-Moody algebra. Our first construction defines a functor from the category of Whittaker modules over the Levi factor of a parabolic subalgebra to the category of modules over the Affine Lie algebra. The second functor sends tensor products of a module over the affine part of the Levi factor (in particular any weight module) and of a Whittaker module over the complement Heisenberg subalgebra to the Affine Lie algebra modules. Both functors preserves irreducibility when the central charge is nonzero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-24T12:24:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67"
    ],
    "keywords": [
      "affine lie algebras representations",
      "whittaker module",
      "levi factor",
      "second functor sends tensor products",
      "affine lie algebra modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}