{
  "id": "2311.13153",
  "version": "v1",
  "published": "2023-11-22T04:31:26.000Z",
  "updated": "2023-11-22T04:31:26.000Z",
  "title": "Unique Factorization For Tensor Products of Parabolic Verma Modules",
  "authors": [
    "K. N. Raghavan",
    "V. Sathish Kumar",
    "R. Venkatesh",
    "Sankaran Viswanath"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra with Cartan subalgebra $\\mathfrak{h}$. We prove a unique factorization property for tensor products of parabolic Verma modules. More generally, we prove unique factorization for products of characters of parabolic Verma modules when restricted to certain subalgebras of $\\mathfrak{h}$. These include fixed point subalgebras of $\\mathfrak{h}$ under subgroups of diagram automorphisms of $\\mathfrak{g}$ and twisted graph automorphisms in the affine case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T04:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B67",
      "17B10"
    ],
    "keywords": [
      "parabolic verma modules",
      "tensor products",
      "symmetrizable kac-moody lie algebra",
      "unique factorization property",
      "fixed point subalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}