{
  "id": "2003.05639",
  "version": "v1",
  "published": "2020-03-12T06:44:45.000Z",
  "updated": "2020-03-12T06:44:45.000Z",
  "title": "Gröbner basis for fusion products",
  "authors": [
    "Johannes Flake",
    "Ghislain Fourier",
    "Viktor Levandovskyy"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.AC",
    "math.CO"
  ],
  "abstract": "We provide a new approach towards the analysis of the fusion products defined by B.Feigin and S.Loktev in the representation theory of (truncated) current Lie algebras. We understand the fusion product as a degeneration using Gr\\\"obner theory of non-commutative algebras and outline a strategy on how to prove a conjecture about the defining relations for the fusion product of two evaluation modules. We conclude with following this strategy for $\\mathfrak{sl}_2(\\mathbb{C}[t]) $ and hence provide yet another proof for the conjecture in this case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-12T06:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "13D02",
      "13D10",
      "05E05"
    ],
    "keywords": [
      "fusion product",
      "gröbner basis",
      "current lie algebras",
      "evaluation modules",
      "representation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}