{
  "id": "math/0112062",
  "version": "v2",
  "published": "2001-12-06T18:33:19.000Z",
  "updated": "2002-01-24T23:28:46.000Z",
  "title": "From Littlewood-Richardson coefficients to cluster algebras in three lectures",
  "authors": [
    "Andrei Zelevinsky"
  ],
  "comment": "Latex, 17 pages, Theorem 3.2 corrected",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "This is an expanded version of the notes of my three lectures at a NATO Advanced Study Institute ``Symmetric functions 2001: surveys of developments and perspectives\" (Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; June 25-July 6, 2001). Lecture I presents a unified expression due to A. Berenstein and the author for generalized Littlewood-Richardson coefficients (= tensor product multiplicities) for any complex semisimple Lie algebra. Lecture II outlines a proof of this result; the main idea of the proof is to relate the LR-coefficients with canonical bases and total positivity. Lecture III introduces cluster algebras, a new class of commutative algebras introduced by S. Fomin and the author in an attempt to create an algebraic framework for canonical bases and total positivity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-01-24T23:28:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster algebras",
      "total positivity",
      "complex semisimple lie algebra",
      "nato advanced study institute",
      "tensor product multiplicities"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12062Z"
    }
  }
}