{
  "id": "1009.3040",
  "version": "v2",
  "published": "2010-09-15T21:07:29.000Z",
  "updated": "2011-10-20T16:28:06.000Z",
  "title": "Symmetric quivers, invariant theory, and saturation theorems for the classical groups",
  "authors": [
    "Steven V Sam"
  ],
  "comment": "29 pages, no figures; v2: updated Theorem 2.4 to odd characteristic, added Remark 3.9, added references, corrected some definitions and typos",
  "journal": "Adv. Math. 229 (2012), no. 2, 1104-1135",
  "doi": "10.1016/j.aim.2011.10.009",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \\lambda^1, ..., \\lambda^r such that the tensor product V_{N\\lambda^1} \\otimes ... \\otimes V_{N\\lambda^r} contains nonzero G-invariants for some N \\ge 1, we show that the tensor product V_{2\\lambda^1} \\otimes ... \\otimes V_{2\\lambda^r} also contains nonzero G-invariants. This extends results of Kapovich-Millson and Belkale-Kumar and complements similar results for the general linear group due to Knutson-Tao and Derksen-Weyman. Our techniques involve the invariant theory of quivers equipped with an involution and the generic representation theory of certain quivers with relations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-20T16:28:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "20G05",
      "15A72",
      "14L30",
      "05E10"
    ],
    "keywords": [
      "invariant theory",
      "saturation theorems",
      "symmetric quivers",
      "classical groups",
      "contains nonzero g-invariants"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Adv. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.3040S"
    }
  }
}