{
  "id": "2103.02836",
  "version": "v1",
  "published": "2021-03-04T05:12:14.000Z",
  "updated": "2021-03-04T05:12:14.000Z",
  "title": "Rigid reflections of rank 3 Coxeter groups and reduced roots of rank 2 Kac--Moody algebras",
  "authors": [
    "Kyu-Hwan Lee",
    "Jeongwoo Yu"
  ],
  "comment": "31 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, the rigid reflections are related to the rigid representations of the quiver. For a family of rank $3$ Coxeter groups, it was conjectured in the same paper that there is a natural bijection from the set of reduced positive roots of a symmetric rank $2$ Kac--Moody algebra onto the set of rigid reflections of the corresponding rank $3$ Coxeter group. In this paper, we prove the conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-04T05:12:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "17B67",
      "20F55",
      "51F15"
    ],
    "keywords": [
      "rigid reflections",
      "kac-moody algebra",
      "reduced roots",
      "coxeter group arises",
      "riemann surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}