{
  "id": "1701.05746",
  "version": "v1",
  "published": "2017-01-20T10:18:41.000Z",
  "updated": "2017-01-20T10:18:41.000Z",
  "title": "Glider representations of chains of semisimple Lie algebras",
  "authors": [
    "Frederik Caenepeel"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We start the study of glider representations in the setting of semisimple Lie algebras. A glider representation is defined for some positively filtered ring $FR$ and here we consider the right bounded algebra filtration $FU(\\mathfrak{g})$ on the universal enveloping algebra $U(\\mathfrak{g})$ of some semisimple Lie algebra $\\mathfrak{g}$ given by a fixed chain of semisimple sub Lie algebras $\\mathfrak{g}_1 \\subset \\mathfrak{g}_2 \\subset \\ldots \\subset \\mathfrak{g}_n = \\mathfrak{g}$. Inspired by the classical representation theory, we introduce so-called Verma glider representations. Their existence is related to the relations between the root systems of the appearing Lie algebras $\\mathfrak{g}_i$. In particular, we consider chains of simple Lie algebras of the same type $A,B,C$ and $D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-20T10:18:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B22"
    ],
    "keywords": [
      "semisimple lie algebra",
      "semisimple sub lie algebras",
      "simple lie algebras",
      "right bounded algebra filtration",
      "verma glider representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}